Σ-Associated Primes over Extension Rings  

作　　者：Lunqun OUYANG Jinwang LIU Yueming XIANG 

机构地区：[1]Department of Mathematics,Hunan University of Science and Technology [2]Department of Mathematics and Applied Mathematics,Huaihua University

出　　处：《Journal of Mathematical Research with Applications》2015年第5期505-520,共16页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11071062);the Scientific Research Fundation of Hunan Provincial Education Department(Grant No.12B101)

摘　　要：In this paper we introduce a concept,called Σ-associated primes,that is a generalization of both associated primes and nilpotent associated primes.We first observe the basic properties of Σ-associated primes and construct typical examples.We next describe all Σ-associated primes of the Ore extension R[x; α,δ],the skew Laurent polynomial ring R[x,x-1; α] and the skew power series ring R[[x; α]],in terms of the Σ-associated primes of R in a very straightforward way.Consequently several known results relating to associated primes and nilpotent associated primes are extended to a more general setting.In this paper we introduce a concept,called Σ-associated primes,that is a generalization of both associated primes and nilpotent associated primes.We first observe the basic properties of Σ-associated primes and construct typical examples.We next describe all Σ-associated primes of the Ore extension R[x; α,δ],the skew Laurent polynomial ring R[x,x-1; α] and the skew power series ring R[[x; α]],in terms of the Σ-associated primes of R in a very straightforward way.Consequently several known results relating to associated primes and nilpotent associated primes are extended to a more general setting.

关 键 词：nilpotent polynomial proof Extension compatible commutative rings generalization automorphism Associated 

分 类 号：O156[理学—数学]