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

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Smalø S., Valenta A.

Colloquium Mathematicum

2007

tom 108

nr 1

63-71

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Smalø S.

1 Valenta A.

1 2007

Wyniki wyszukiwania

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