The grothendieck group of the category of modules of finite projective dimension over certain weakly triangular algebras
作者:
Eduardo N. Marcos,
Héctor A. Merklen,
María I. Platzeck,
期刊:
Communications in Algebra
(Taylor Available online 2000)
卷期:
Volume 28,
issue 3
页码: 1387-1404
ISSN:0092-7872
年代: 2000
DOI:10.1080/00927870008826901
出版商: Gordon and Breach Science Publishers Ltd.
数据来源: Taylor
摘要:
In this paper we study the category of finitely generated modules of finite projective dimension over a class of weakly triangular algebras, which includes the algebras whose idempotent ideals have finite projective dimension. In particular, we prove that the relations given by the (relative) almost split sequences generate the group of all relations for the Grothendieck group ofP<∞(Λ) if and only ifP<∞(Λ) is of finite type. A similar statement is known to hold for the category of all finitely generated modules over an artin algebra, and was proven by C.M.Butler and M. Auslander ( [B] and [A]).
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