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The fast dissolution of certain calcium-containing compounds makes them attractive carriers for trace minerals in nutritional applications, e.g., iron and zinc to alleviate mineral deficiencies in affected people. Here, CaO-based nanostructured mixed oxides containing nutritionally relevant amounts of Fe, Zn, Cu, and Mn were produced by one-step flame spray pyrolysis. The compounds were characterized by nitrogen adsorption, x-ray diffraction, (scanning) transmission electron microscopy, and thermogravimetric analysis. Dissolution in dilute acid (i.d.a.) was measured as an indicator of their in vivo bioavailability. High contents of calcium resulted in matrix encapsulation of iron and zinc preventing formation of poorly soluble oxides. For 3.6 ≤ Ca:Fe ≤ 10.8, Ca2Fe2O5 coexisted with CaO. For Ca/Zn compounds, no mixed oxides were obtained, indicating that the Ca/Zn composition can be tuned without affecting their solubility i.d.a. Aging under ambient conditions up to 225 days transformed CaO to CaCO3 without affecting iron solubility i.d.a. Furthermore, Cu and Mn could be readily incorporated in the nanostructured CaO matrix. All such compounds dissolved rapidly and completely i.d.a., suggesting good in vivo bioavailability.
Let G be a group such that, for any subgroup H of G, every automorphism of H can be extended to an automorphism of G. Such a group G is said to be of injective type. The finite abelian groups of injective type are precisely the quasi-injective groups. We prove that a finite non-abelian group G of injective type has even order. If, furthermore, G is also quasi-injective, then we prove that G = K × B, with B a quasi-injective abelian group of odd order and either K = Q8 (the quaternion group of order 8) or K = Dih(A), a dihedral group on a quasi-injective abelian group A of odd order coprime with the order of B. We give a description of the supersoluble finite groups of injective type whose Sylow 2-subgroup are abelian showing that these groups are, in general, not quasi-injective. In particular, the characterisation of such groups is reduced to that of finite 2-groups that are of injective type. We give several restrictions on the latter. We also show that the alternating group A5 is of injective type but that the binary icosahedral group SL(2, 5) is not.
Iron deficiency affects approximately 2 billion people worldwide, especially young women and children. Food fortification with iron is a sustainable approach to alleviate iron deficiency but remains a challenge. Water-soluble compounds with high bioavailability (e.g. the “gold standard” FeSO4) usually cause unacceptable sensory changes in foods, while compounds that are less reactive in food matrices are often less bioavailable. Solubility (and therefore bioavailability) can be improved by increasing the specific surface area (SSA) of the compound, i.e. decreasing its particle size to the nm range. Here, iron oxide-based nanostructured compounds with Mg or Ca are made using scalable flame aerosol technology. Addition of either element increased iron solubility to a level comparable to iron phosphate. Furthermore, these additions lightened the powder color and sensory changes in fruit yoghurt were less prominent than for FeSO4.
This article analyzes the iconography on a ceramic vessel collected
from the site of Los Naranjos, Honduras, over 70 years ago by Danish
archaeologist Jens Yde. The relatively more naturalistic representation of
the scene on the vessel allows us to interpret the motifs called
“dancing figures” as relating to a well-documented corpus of
Mesoamerican origin mythology. We then turn our attention to the site of
Los Naranjos and document the fact that the area of Lake Yojoa closely
mirrors the idealized Mesoamerican landscape associated with the place of
the earth's creation. Combining this insight with the depiction on
the Yde vessel, we suggest that the Cave of Tauleve may have been
considered the place of human creation or human emergence.
A complete structural characterization of submonoids $S$ of a polycyclic-by-finite group such that the semigroup algebra $K[S]$ over a field $K$ is right noetherian is obtained. It follows that such algebras are also left noetherian.
A class of Noetherian semigroup algebras K[S] is described. In particular, we show that, for any submonoid S of the semigroup Mn of all monomial n × n matrices over a polycyclic-by-finite group G, K[S] is right Noetherian if and only if S satisfies the ascending chain condition on right ideals. This is then used to prove that every prime homomorphic image of a semigroup algebra of a finitely generated Malcev nilpotent semigroup S satisfying the ascending chain condition on right ideals is left and right Noetherian.
Let S be a semigroup and let be an S-graded ring. Rs = 0 for all but finitely many elements s ∈ S1, then R is said to have finite support. In this paper we concern ourselves with the question of whether a graded ring R with finite support inherits a given ring theoretic property from the homogeneous subrings Re corresponding to idempotent semigroup elements e.
E Jespers, Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NF, Canada A1C 5S7,
M M Parmenter, Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NF, Canada A1C 5S7,
P F Smith, Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland
A description is given of the unit group for the two groups G = D12 and G = D8 × C2. In particular, it is shown that in both cases the bicyclic units generate a torsion-free normal complement. It follows that the Bass-cyclic units together with the bicyclic units generate a subgroup of finite index in for all n ≥ 3.
Let A be a subring of a commutative ring B. If the natural mapping from the prime spectrum of B to the prime spectrum of A is injective (respectively bijective) then the pair (A, B) is said to have the injective (respectively bijective) Spec-map. We give necessary and sufficient conditions for a pair of rings A and B graded by a free abelian group to have the injective (respectively bijective) Spec-map. For this we first deal with the polynomial case. Let l be a field and k a subfield. Then the pair of polynomial rings (k[X], l[X]) has the injective Spec-map if and only if l is a purely inseparable extension of k.
Let G be a finite group, (ZG) the group of units of the integral group ring ZG and 1(ZG) the subgroup of units of augmentation 1. In this paper, we are primarily concerned with the problem of describing constructively (ZG) for particular groups G. This has been done for a small number of groups (see  for an excellent survey), and most recently Jespers and Leal  described (ZG) for several 2-groups. While the situation is clear for all groups of order less than 16, not all groups of order 16 were discussed in their paper. Our main aim is to complete the description of (ZG) for all groups of order 16. Since the structure of the unit group of abelian groups is very well known (see for example ), we are only interested in the non-abelian case.
Directly indecomposable absolute subretracts that are commutative Noetherian rings are described. This is an application of our main result characterizing unital directly indecomposable absolute subretracts which contain a maximal ideal with nonzero annihilator.
In this brief note, we will show how in principle to find all units in the integral group ring ZG, whenever G is a finite group such that and Z(G) each have exponent 2, 3, 4 or 6. Special cases include the dihedral group of order 8, whose units were previously computed by Polcino Milies , and the group discussed by Ritter and Sehgal . Other examples of noncommutative integral group rings whose units have been computed include , but in general very little progress has been made in this direction. For basic information on units in group rings, the reader is referred to Sehgal .
The following questions are studied: When is a semigroup graded ring left Noetherian, respectively semiprime left Goldie? Necessary sufficient conditions are proved for cancellative semigroup-graded subrings of rings weakly or strongly graded by a polycyclic-by-finite (unique product) group. For semigroup rings R[S] we also give a solution to the problem in case S is an inverse semigroup.
A set of comprehensive computer models for the chemical evolution of galaxies have been used to determine the limits on the amount of mass that could exist in the form of dark stellar remnants deriving from normal stellar evolutionary processes. In these models, the instantaneous recycling approximation is not assumed: stars are binned into 10 mass intervals, with different lifetimes, yields and remnant masses. The models were run using many different values for the IMF (including non-Salpeter and varying IMFs), star formation rates, yields, remnant masses, gas infall and outflow rates, primordial metalliciy and initial conditions. The Galaxy is described by a two-zone halo-disk system, where gas from the halo falls onto the disk. Elliptical galaxies are described by single-zone models.
The notion of an almost Krull domain is extended to rings satisfying a polynomial identity. Some general structural results are obtained. We also prove that skew polynomial rings R [ X, σ] remain almost Krull if R is an almost Krull ring. Finally, we study when semigroup ring R[S] are almost Krull rings, in the case when the group of quotients of S has the ascending chain condition on cyclic subgroups. An example is included to show that the general (semi-) group ring case is much more difficult to deal with.
We give a complete description of the Brown–McCoy radical of a semigroup ring R[S], where R is an arbitrary associative ring and S is a commutative cancellative semigroup; in particular we obtain the answer to a question of E. Puczyłowski stated in 
Throughout this note all rings R are associative with unity 1; all semigroups S are commutative and cancellative with unity. Note that the condition that R and S have a unity can be dropped (cf. ). The quotient group of S is denoted by Q(S). We say that S is torsion free (resp. has torsion free rank n) if Q(S) is torsion free (resp. has torsion free rank n). The Brown–McCoy radical (i.e. the upper radical determined by the class of all simple rings with unity) of a ring R is denoted by u(R). We refer to  for further detail on radicals and in particular on the Brown–McCoy radical.
First we state some well-known results and a preliminary lemma. Let R and T be rings with the same unity such that R ⊂ T. Then T is said to be a normalizing extension of R if T = Rx1+…+Rxn for certain elements x1, …, xn of T and Rxi = xiR for all i such that 1 ∨i∨n. If all xi are central in T, then we say that T is a central normalizing extension of R.
The aim of this note is to study the class group of a central Ω-Krull ring and to determine in some cases whether a twisted (semi) group ring is a central Ω-Krull ring. In  we defined an Ω-Krull ring as a generalization of a commutative Krull domain. In the commutative theory, the class group plays an important role. In the second and third section, we generalize some results to the noncommutative case, in particular the relation between the class group of a central Ω-Krull ring and the class group of a localization. Some results are obtained in case the ring is graded. Theorem 3.2 establishes the relation between the class group and the graded class group. In particular, in the P.I. case we obtain that the class group is equal to the graded class group. As a consequence of a result on direct limits of Ω-Krull rings, we are able to derive a necessary and sufficient condition in order that a polynomial ring R[(Xi)i∊I] (I may be infinite) is a central Ω-Krull ring.
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