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• # Artykuł - szczegóły

## Colloquium Mathematicum

2007 | 108 | 1 | 63-71

## Top-stable and layer-stable degenerations and hom-order

EN

### Abstrakty

EN
Using geometrical methods, Huisgen-Zimmermann showed that if M is a module with simple top, then M has no proper degeneration $M <_{deg} N$ such that $𝔯^{t}M/𝔯^{t+1}M ≃ 𝔯^{t}N/𝔯^{t+1}N$ for all t. Given a module M with square-free top and a projective cover P, she showed that $dim_{k}Hom(M,M) = dim_{k}Hom(P,M)$ if and only if M has no proper degeneration $M <_{deg} N$ where M/𝔯M ≃ N/𝔯N. We prove here these results in a more general form, for hom-order instead of degeneration-order, and we prove them algebraically. The results of Huisgen-Zimmermann follow as consequences from our results. In particular, we find that her second result holds not just for modules with square-free top, but also for indecomposable modules in general.

63-71

wydano
2007

### Twórcy

autor
• Department of Mathematical Sciences, University of Science and Technology, N-7491 Trondheim, Norway
autor
• Department of Mathematical Sciences, University of Science and Technology, N-7491 Trondheim, Norway