QUASITILTED EXTENSIONS BY NONDIRECTING MODULES

Autor:	Inger Heidi Slungård, Ole Enge, Sverre O. Smalo
Rok vydání:	2001
Předmět:	Discrete mathematics Pure mathematics Algebra and Number Theory Division algebra Extension (predicate logic) Algebra over a field Indecomposable module Mathematics
Zdroj:	Communications in Algebra. 29:593-610
ISSN:	1532-4125 0092-7872
DOI:	10.1081/agb-100001526
Popis:	Let M be an indecomposable nondirecting module over a finite dimensional k-algebra Λ, and form the extension of Λ by the Λ–G-bimodule M, where G ⊆ EndΛ (M)op. We will show that if such an extension is quasitilted, then G = EndΛ (M)op and G is a division algebra. We also show that the double extension of Λ by M is not quasitilted, where G = EndΛ (M)op. So for every indecomposable nondirecting Λ-module M it is not possible to extend Λ with M more than once and still get a quasitilted algebra. If M is a nonzero decomposable Λ-module and is quasitilted, we then show that M is either directing or M has to be of a special form.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::8bce082f2ed855353cb10882ebe7e0e8 https://doi.org/10.1081/agb-100001526 Zobrazit plný text záznamu