On degenerations of modules

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13 Citations (Scopus)

Abstract

We generalize a result of Zwara concerning the degeneration of modules over Artinian algebras to that over general algebras. In fact, let R be any algebra over a field and let M and N be finitely generated left R-modules. Then, we show that M degenerates to N if and only if there is a short exact sequence of finitely generated left R-modules 0→Z→ φ ψ M⊕Z→N→0 such that the endomorphism ψ on Z is nilpotent. We give several applications of this theorem to commutative ring theory.

Original languageEnglish
Pages (from-to)217-226
Number of pages10
JournalJournal of Algebra
Volume278
Issue number1
DOIs
Publication statusPublished - Aug 1 2004

ASJC Scopus subject areas

  • Algebra and Number Theory

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