Let R is a noetherian ring,M is a finitely generated R-module.This paper studies the relation between associated prime Ass(M/N)and annihilator Ann(M/N),and has given the necessary and sufficient conditions of Ass(M/N)...Let R is a noetherian ring,M is a finitely generated R-module.This paper studies the relation between associated prime Ass(M/N)and annihilator Ann(M/N),and has given the necessary and sufficient conditions of Ass(M/N)=Ann(M/N).展开更多
It is well-known that a ring R is right Noetherian if and only if every direct sum of injective right R-modules is injective. In this paper, we will characterize Ne-Noetherian rings and U-Noetherian rings by Ne-inject...It is well-known that a ring R is right Noetherian if and only if every direct sum of injective right R-modules is injective. In this paper, we will characterize Ne-Noetherian rings and U-Noetherian rings by Ne-injective modules and U-injective modules.展开更多
Let (S,≤) be a strictly totally ordered monoid which is also artinian, and R a right noetherian ring. Assume that M is a finitely generated right R-module and N is a left Rmodule. Denote by [[MS,≤]] and [NS,≤] the ...Let (S,≤) be a strictly totally ordered monoid which is also artinian, and R a right noetherian ring. Assume that M is a finitely generated right R-module and N is a left Rmodule. Denote by [[MS,≤]] and [NS,≤] the module of generalized power series over M, and the generalized Macaulay-Northcott module over N, respectively. Then we show that there exists an isomorphism of Abelian groups:Tori[[ RS,≤]]([[MS,≤]],[NS,≤])≌ s∈S ToriR (M,N).展开更多
Let R be a left and right Noetherian ring and n, k be any non-negative integers. R is said to satisfy the Auslander-type condition Gn（k） if the right fiat dimension of the （i ＋ 1）-th term in a minimal injective r...Let R be a left and right Noetherian ring and n, k be any non-negative integers. R is said to satisfy the Auslander-type condition Gn（k） if the right fiat dimension of the （i ＋ 1）-th term in a minimal injective resolution of RR is at most i ＋ k for any 0 ≤ i ≤ n - 1. In this paper, we prove that R is Gn（k） if and only if so is a lower triangular matrix ring of any degree t over R.展开更多
文摘Let R is a noetherian ring,M is a finitely generated R-module.This paper studies the relation between associated prime Ass(M/N)and annihilator Ann(M/N),and has given the necessary and sufficient conditions of Ass(M/N)=Ann(M/N).
基金the National Natural Science Foundation of China(10171082)
文摘It is well-known that a ring R is right Noetherian if and only if every direct sum of injective right R-modules is injective. In this paper, we will characterize Ne-Noetherian rings and U-Noetherian rings by Ne-injective modules and U-injective modules.
基金the National Natural Science Foundation of China (No.10961021)the Teaching and Research Award Program for Outsanding Young Teachers in Higher Education Institutions of Ministry of Education(No.NCET-02-080)
文摘Let (S,≤) be a strictly totally ordered monoid which is also artinian, and R a right noetherian ring. Assume that M is a finitely generated right R-module and N is a left Rmodule. Denote by [[MS,≤]] and [NS,≤] the module of generalized power series over M, and the generalized Macaulay-Northcott module over N, respectively. Then we show that there exists an isomorphism of Abelian groups:Tori[[ RS,≤]]([[MS,≤]],[NS,≤])≌ s∈S ToriR (M,N).
基金supported by the Specialized Research Fund for the Doctoral Pro-gram of Higher Education(Grant No.20100091110034)National Natural Science Foundation of China(Grant Nos.11171142,11126169,11101217)+2 种基金Natural Science Foundation of Jiangsu Province of China(Grant Nos.BK2010047,BK2010007)the Scientific Research Fund of Hunan Provincial Education Department(Grant No.10C1143)a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘Let R be a left and right Noetherian ring and n, k be any non-negative integers. R is said to satisfy the Auslander-type condition Gn（k） if the right fiat dimension of the （i ＋ 1）-th term in a minimal injective resolution of RR is at most i ＋ k for any 0 ≤ i ≤ n - 1. In this paper, we prove that R is Gn（k） if and only if so is a lower triangular matrix ring of any degree t over R.
