Excellent Extensions and Homological Conjectures  

作　　者：Yingying Zhang 

机构地区：[1]Department of Mathematics,Hohai University,Nanjing 210098,China

出　　处：《Algebra Colloquium》2018年第4期619-626,共8页代数集刊（英文版）

摘　　要：In this paper,we introduce the notion of excellent extensions of rings.Let F be an excellent extension of an Artin algebra∧,we prove that∧satisfies the Gorenstein symmetry conjecture(resp.,finitistic dimension conjecture,Auslander-Gorenstein conjecture,Nakayama conjecture)if and only if so does F.As a special case of excellent extensions,when G is a finite group whose order is invertible in∧acting on∧and∧is G-stable,we prove that if the skew group algebra∧G satisfies strong Nakayama conjecture(resp.,generalized Nakayama conjecture),then so does∧.

关 键 词：EXCELLENT EXTENSION SKEW group ALGEBRA homological CONJECTURE 

分 类 号：O1[理学—数学]