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

• Autorzy: S. O. Smalø , A. Valenta
• Języki publikacji: 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.

Kategorie tematyczne

• 16D10: General module theory
• 16G20: Representations of quivers and partially ordered sets
• 14L30: Group actions on varieties or schemes (quotients)
• 16E30: Homological functors on modules (Tor, Ext, etc.)
• 16G10: Representations of Artinian rings

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2007
• Tom: 108
• Numer: 1
• Strony: 63-71

Daty

wydano

2007

Twórcy

autor

S. O. Smalø

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

autor

A. Valenta

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

Identyfikatory

DOI

10.4064/cm108-1-6