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Reports Year : 2011

Free Cyclic Submodules and Non-Unimodular Vectors

Abstract

Given a finite associative ring with unity, $R$, and its two-dimensional left module, $^{2}R$, the following two problems are addressed: 1) the existence of vectors of $^{2}R$ that do not belong to any free cyclic submodule (FCS) generated by a unimodular vector and 2) conditions under which such (non-unimodular) vectors generate FCSs. The main result is that for a non-unimodular vector to generate an FCS of $^{2}R$, $R$ must have at least two maximal right ideals of which at least one is non-principal.
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Dates and versions

hal-00608865 , version 1 (15-07-2011)
hal-00608865 , version 2 (12-08-2011)

Identifiers

  • HAL Id : hal-00608865 , version 1

Cite

Joanne Hall, Metod Saniga. Free Cyclic Submodules and Non-Unimodular Vectors. 2011. ⟨hal-00608865v1⟩
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