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Extensions that are Submodules of their Quotients

Published online by Cambridge University Press:  20 November 2018

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

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1990

References

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