Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-24T19:17:51.978Z Has data issue: false hasContentIssue false
  • English
  • Français

Extensions that are Submodules of their Quotients

Published online by Cambridge University Press:  20 November 2018

F. Okoh  and
F. Zorzitto
F. Okoh
Affiliation:
Department of Mathematics, Wayne State University, Detroit, Michigan, 48202, U.S.A.
F. Zorzitto
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let 0 → N → E → F → 0 be a short exact sequence of torsion-free Kronecker modules. Suppose that N and F have rank one. The module F is classified by a height function h defined on the projective line. If N is finite-dimensional, h is supported on a set of cardinality less than that of its domain and h takes on the value ∞, then E embeds into F. The converse holds if all such E embed into F. This embeddability is in contrast to the situation with other rings such as commutative domains, where it never occurs.

Keywords

16A6416A46
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 1 , 01 March 1990 , pp. 93 - 99
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Aronszajn, N., Fixman, U., Algebraic spectral problems, Studia Math. 30 (1968), 273–338.Google Scholar
2. Fixman, U., On algebraic equivalence between pairs of linear transformations, Trans. Amer. Math. Soc. 113, 3 (1964), 424–453.Google Scholar
3. Lawrence, J., Okoh, F., Zorzitto, F., Rational functions and Kronecker modules, Comm. in Alg. 14, 10 (1986), 1947–1965.Google Scholar
4. Okoh, F., Some properties of purely simple Kronecker modules I, J. Pure Appl. Alg. 27 (1983), 39–18.Google Scholar
5. Okoh, F., Applications of linear junctionals to Kronecker modules I, Lin. Alg. Appl. 76 (1986), 165— 188.Google Scholar
6. Okoh, F., Zorzitto, F., Modules for which the endomorphism rings are integral domains, to appear.Google Scholar
7. Ringel, C. M., Infinite dimensional representations of finite dimensional hereditary algebras, Symposia Mathematica, 23 (1979), 321–412.Google Scholar