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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
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Abstract

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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

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