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Environmental exposures during pregnancy may increase breast cancer risk for mothers and female offspring. Tumor tissue assays may provide insight regarding the mechanisms. This study assessed the feasibility of obtaining tumor samples and pathology reports from mothers (F0) who were enrolled in the Child Health and Development Studies during pregnancy from 1959 to 1967 and their daughters (F1) who developed breast cancer over more than 50 years of follow-up. Breast cancer cases were identified through linkage to the California Cancer Registry and self-report. Written consent was obtained from 116 F0 and 95 F1 breast cancer survivors to access their pathology reports and tumor blocks. Of those contacted, 62% consented, 13% refused and 24% did not respond. We obtained tissue samples for 57% and pathology reports for 75%, and if diagnosis was made ⩽10 years we obtained tissue samples and pathology reports for 91% and 79%, respectively. Obtaining pathology reports and tumor tissues of two generations is feasible and will support investigation of the relationship between early-life exposures and molecular tumor markers. However, we found that more recent diagnosis increased the accessibility of tumor tissue. We recommend that cohorts request consent for obtaining future tumor tissues at study enrollment and implement real-time tissue collection to enhance success of collecting tumor samples and data.
Growing evidence indicates that parental smoking is associated with risk of offspring obesity. The purpose of this study was to identify whether parental tobacco smoking during gestation was associated with risk of diabetes mellitus. This is a prospective study of 44- to 54-year-old daughters (n=1801) born in the Child Health and Development Studies pregnancy cohort between 1959 and 1967. Their mothers resided near Oakland California, were members of the Kaiser Foundation Health Plan and reported parental tobacco smoking during an early pregnancy interview. Daughters reported physician diagnoses of diabetes mellitus and provided blood samples for hemoglobin A1C measurement. Prenatal maternal smoking had a stronger association with daughters’ diabetes mellitus risk than prenatal paternal smoking, and the former persisted after adjustment for parental race, diabetes and employment (aRR=2.4 [95% confidence intervals 1.4–4.1] P<0.01 and aRR=1.7 [95% confidence intervals 1.0–3.0] P=0.05, respectively). Estimates of the effect of parental smoking were unchanged when further adjusted by daughters’ birth weight or current body mass index (BMI). Maternal smoking was also significantly associated with self-reported type 2 diabetes diagnosis (2.3 [95% confidence intervals 1.0–5.0] P<0.05). Having parents who smoked during pregnancy was associated with an increased risk of diabetes mellitus among adult daughters, independent of known risk factors, providing further evidence that prenatal environmental chemical exposures independent of birth weight and current BMI may contribute to adult diabetes mellitus. While other studies seek to confirm our results, caution toward tobacco smoking by or proximal to pregnant women is warranted in diabetes mellitus prevention efforts.
During two legionellosis outbreak investigations, one at a geriatric centre and the other in high-rise housing for seniors, it was observed that additional cases of legionellosis occurred in nearby smaller residential settings. This apparent geographical cluster of legionellosis occurred in the same general area of a community water storage tank. No potential airborne sources in or near the area could be identified, but a community water system storage tank that was centrally located among case residences spurred an investigation of water-quality factors in the identified investigation area. Conditions conducive for Legionella growth, particularly low chlorine residuals, were found. The rate of legionellosis among residents aged ⩾50 years in the investigation areas (61·0 and 64·1/100 000) was eight times higher than in the rest of the service area (9·0/100 000) and almost 20 times higher than the statewide annual average incidence rate (3·2/100 000). A water mains flushing programme in the area was launched by the water utility, and water samples taken before and during flushing found L. pneumophila.
This issue of the Journal features collaborative follow-up studies of two unique pregnancy cohorts recruited during 1959–1966 in the United States. Here we introduce the Early Determinants of Adult Health (EDAH) study. EDAH was designed to compare health outcomes in midlife (age 40s) for same-sex siblings discordant on birthweight for gestational age. A sufficient sample of discordant siblings could only be obtained by combining these two cohorts in a single follow-up study. All of the subsequent six papers are either based upon the EDAH sample or are related to it in various ways. For example, three papers report results from studies that significantly extended the ‘core’ EDAH sample to address specific questions.
We first present the overall design of and rationale for the EDAH study. Then we offer a synopsis of past work with the two cohorts to provide a context for both EDAH and the related studies. Next, we describe the recruitment and assessment procedures for the core EDAH sample. This includes the process of sampling and recruitment of potential participants; a comparison of those who were assessed and not assessed based on archived data; the methods used in the adult follow-up assessment; and the characteristics at follow-up of those who were assessed. We provide online supplementary tables with much further detail. Finally, we note further work in progress on EDAH and related studies, and draw attention to the broader implications of this endeavor.
Fetal exposure to caffeine is associated with adverse pregnancy outcomes. Animal and human studies suggest that caffeine may have effects on the developing reproductive system. Here we report on mothers’ smoking, coffee and alcohol use, recorded during pregnancy, and semen quality in sons in the age group of 38–47 years. Subjects were a subset of the Child Health and Development Studies, a pregnancy cohort enrolled between 1959 and 1967 in the Kaiser Foundation Health Plan near Oakland, California. In 2005, adult sons participated in a follow-up study (n = 338) and semen samples were donated by 196 participants. Samples were analyzed for sperm concentration, motility and morphology according to the National Cooperative Reproductive Medicine Network (Fertile Male Study) Protocol. Mean sperm concentration was reduced by approximately 16 million sperms for sons with high prenatal exposure (5 cups of maternal coffee use per day) compared with unexposed sons (P-value for decreasing trend = 0.09), which translates to a proportionate reduction of 25%. Mean percent motile sperm decreased by approximately 7 points (P-value = 0.04), a proportionate decline of 13%, and mean percent sperm with normal morphology decreased by approximately 2 points (P-value = 0.01), a proportionate decline of 25%. Maternal cigarette and alcohol use were not associated with son's semen quality. Adjusting for son's contemporary coffee, alcohol and cigarette use did not explain the maternal associations. Findings for son's coffee intake and father's prenatal coffee, cigarette and alcohol use were non-significant and inconclusive. These results contribute to the evidence that maternal coffee use during pregnancy may impair the reproductive development of the male fetus.
The first topic of this chapter is commutativity in firs. We shall find that any maximal commutative subring of a 2-fir with strong DFL is integrally closed (Corollary 1.2), and the same method allows us to describe the centres of 2-firs as integrally closed rings and make a study of invariant elements in 2-firs and their factors in Sections 6.1 and 6.2. The well-known result that a simple proper homomorphic image of a principal ideal domain is a matrix ring over a skew field is generalized here to atomic 2-firs (Theorem 2.4). In Section 6.3 the centres of principal ideal domains are characterized as Krull domains. Further, the centre of a non-principal fir is shown to be a field in Section 6.4.
Secondly we look at subalgebras and ideals of free algebras in Section 6.6; by way of preparation submonoids of free monoids are treated in section 6.5. A brief excursion into coding theory shows how the Kraft–McMillan inequality can be used to find free subalgebras, and the fir property of free algebras is again derived (Theorem 6.7). Section 6.7 is devoted to a fundamental theorem on free algebras: Bergman's centralizer theorem (Theorem 7.7).
Section 6.8 deals with invariants under automorphisms of free algebras, and Section 6.9 treats the Galois correspondence between automorphism groups and free subalgebras, as described by Kharchenko.
This appendix gives a brief summary of facts needed from lattice theory, homological algebra and logic, with references to proofs or sometimes the proofs themselves. In each section some reference books are listed, with an abbreviation which is used in quoting them in the appendix.
LT: G. Birkhoff, Lattice Theory, 3rd Edition. Amer. Math. Soc. Providence RI 1967.
BA: P. M. Cohn, Basic Algebra, Groups, Rings and Fields. Springer, London 2002.
FA: P. M. Cohn, Further Algebra and Applications. Springer, London 2003.
UA: P. M. Cohn, Universal Algebra, 2nd Edition. D. Reidel, Dordrecht 1981.
(i) We recall that a lattice is a partially ordered set in which any pair of elements a, b has a supremum (i.e. least upper bound, briefly: sup), also called join and written a ∨ b, and an infimum (i.e. greatest lower bound, briefly: inf), also called meet and written a ∨ b. It follows that in a lattice L every finite non-empty subset has a sup and an inf; if every subset has a sup and an inf, L is said to be complete. A partially ordered set that is a lattice (with respect to the partial ordering) is said to be lattice-ordered. It is possible to define lattices as algebras with two binary operations ∨,∧ satisfying certain identities, so that lattices form a variety of algebras (LT, p. 9, UA, p. 63 or BA, Section 3.1).
For the study of non-commutative unique factorization domains we begin by looking at the lattice of factors and the notion of similarity for matrices in Section 3.1. The resulting concept of non-commutative UFD, in Section 3.2, is mainly of interest for the factorization of full n×n matrices over 2n-firs; thus it can be applied to study factorization in free algebras. Another class, the rigid UFDs, forming the subject of Section 3.3, generalizes valuation rings and is exemplified by free power series rings. We also examine various direct decomposition theorems (Sections 3.4 and 3.5), but throughout this chapter we only consider square (full) matrices, corresponding to torsion modules over semifirs. The factorization of rectangular matrices, which is much less well developed, will be taken up in Chapter 5.
Similarity in semifirs
To study factorizations in non-commutative integral domains it is necessary to consider modules of the form R/aR. We recall from Section 1.3 that two right ideals a, a′ of a ring R are similar if R/a ≅ R/a′. In the case of principal ideals the similarity of aR and a′R (for regular elements a and a′) just corresponds to the similarity of the elements a and a′ as defined in Section 0.5 (see Proposition 0.5.2 and the preceding discussion, as well as Section 1.3).
In a semifir it is possible to simplify this condition still further.
Proving that a polynomial ring in one variable over a field is a principal ideal domain can be done by means of the Euclidean algorithm, but this does not extend to more variables. However, if the variables are not allowed to commute, giving a free associative algebra, then there is a generalization, the weak algorithm, which can be used to prove that all one-sided ideals are free. This book presents the theory of free ideal rings (firs) in detail. Particular emphasis is placed on rings with a weak algorithm, exemplified by free associative algebras. There is also a full account of localization which is treated for general rings but the features arising in firs are given special attention. Each section has a number of exercises, including some open problems, and each chapter ends in a historical note.
This chapter studies ways of embedding rings in fields and more generally, the homomorphisms of rings into fields. For a commutative ring such homomorphisms can be described completely in terms of prime ideals, and we shall see that a similar, but less obvious, description applies to quite general rings.
After some generalities on the rings of fractions obtained by inverting matrices (Section 7.1) and on R-fields and their specializations (Section 7.2), we introduce in Section 7.3 the notion of a matrix ideal. This corresponds to the concept of an ideal in a commutative ring, but has no direct interpretation. The analogue of a prime ideal, the prime matrix ideal, has properties corresponding closely to those of prime ideals, and in Section 7.4 we shall see that the prime matrix ideals can be used to describe homomorphisms of general rings into fields, just as prime ideals are used in the commutative case. This follows from Theorem 4.3, which characterizes prime matrix ideals as ‘singular kernels’, i.e. the sets of matrices that become singular under a homomorphism into some field.
This characterization is applied in section 7.5 to derive criteria for a general ring to be embeddable in a field, or to have a universal field of fractions. These results are used to show that every Sylvester domain (in particular every semifir) has a universal field of fractions.
Since the main classes of rings considered in this work generalize principal ideal domains, it seems reasonable to start by recalling the properties of the latter. We begin in Section 1.1 by looking at examples that will be important to us later, the skew polynomial rings, and in Section 1.2 discuss the division algorithm, which forms a paradigm for later concepts. Sections 1.3 and 1.4 recall well known properties of principal ideal domains and their modules, while Section 1.5 describes the Malcev–Neumann construction of the ordered series field of an ordered group, and the Bergman conjugacy theorem. The concluding Section 1.6 deals with Jategaonkar's iterated skew polynomial rings, leading to one-sided PIDs with a transfinite-valued division algorithm. The later parts of Sections 1.5 and 1.6 are not essential for an understanding of the rest and so may be omitted on a first reading.
Skew polynomial rings
Polynomial rings are familiar to the reader as the rings obtained from commutative rings by adjoining one or more indeterminates. Here we want to discuss a generalization that is often useful in providing examples and counter-examples. It differs from the usual polynomial ring K[x] in one indeterminate x over a field K in that k need not be commutative, nor commute with x.
Just as firs form a natural generalization of principal ideal domains, so there is a class of modules over firs that generalizes the finitely generated modules over principal ideal domains. They are the positive modules studied in Section 5.3; they admit a decomposition into indecomposables, with a Krull–Schmidt theorem (in fact this holds quite generally for finitely presented modules over firs), but it is no longer true that the indecomposables are cyclic. On the other hand, there is a dual class, the negative modules, and we shall see how the general finitely presented module is built up from free modules, positive and negative modules. A basic notion is that of a bound module; this and the duality, essentially the transpose, also used in the representation theory of algebras, are developed in Sections 5.1 and 5.2 in the more general context of hereditary rings. In the special case of free algebras, the endomorphism rings of finitely presented bound modules are shown to be finite-dimensional over the ground field. This result, first proved by J. Lewin, is obtained here by means of a normal form for matrices over a free algebra, due to M. L. Roberts, and his work is described in Section 5.8.
A second topic is the rank of matrices. Several notions of rank are defined, of which the most important, the inner rank, is studied more closely in Section 5.4. Over a semifir the inner rank obeys Sylvester's law of nullity.
This chapter collects some facts on rings and modules, which form neither part of our subject proper, nor part of the general background (described in the Appendix). By its nature the content is rather mixed, and the reader may well wish to begin with Chapter 1 or even Chapter 2, and only turn back when necessary.
In Section 0.1 we describe the conditions usually imposed on the ranks of free modules. The formation of matrix rings is discussed in Section 0.2; Section 0.3 is devoted to projective modules and the special class of Hermite rings is considered in Section 0.4.
Section 0.5 deals with the relation between a module and its defining matrix, and in particular the condition for two matrices to define isomorphic modules. This and the results on eigenrings and centralizers in Section 0.6 are mainly used in Chapters 4 and 6.
The Ore construction of rings of fractions is behind much of the later development, even when this does not appear explicitly. In Section 0.7 we recall the details and apply it in Section 0.8 to modules over Ore domains; it turns out that the (left or right) Ore condition has some unexpected consequences. In Section 0.9 we recall some well-known facts on factorization in commutative rings, often stated in terms of monoids, in a form needed later.