### 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 language | English |
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Pages (from-to) | 217-226 |

Number of pages | 10 |

Journal | Journal of Algebra |

Volume | 278 |

Issue number | 1 |

DOIs | |

Publication status | Published - Aug 1 2004 |

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Yoshino, Y. (2004). On degenerations of modules.

*Journal of Algebra*,*278*(1), 217-226. https://doi.org/10.1016/j.jalgebra.2003.10.020