# Degenerations for Modules Over Representation-Finite Algebras

## Proceedings of the American Mathematical Society / v.127 no.5. 1999, pp.1313-1322 window.___gcfg = {lang: 'ko'}; (function() { var po = document.createElement('script'); po.type = 'text/javascript'; po.async = true; po.src = 'https://apis.google.com/js/platform.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(po, s); })();

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Abstract : Let A be a representation-finite algebra. We show that a finite dimensional A-module M degenerates to another A-module N if and only if the inequalities dim $_{K}$ Hom $_{A}$ (M, X) $\leq$ dim $_{K}$ Hom $_{A}$ (N, X) hold for all A-modules X. We prove also that if Ext $_{A}^{1}$ (X, X) = 0 for any indecomposable A-module X, then any degeneration of A-modules is given by a chain of short exact sequences.

Keyword : Primary 14L30, 16G60, 16G70

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