共查询到19条相似文献,搜索用时 62 毫秒
1.
设A(て)B是整环的扩张,(S,≤)是满足一定条件的严格偏序幺半群,[[BS,≤]]是整环B上的广义幂级数环.本文研究整环[Bs,≤]]和{f∈[[Bs,≤]]|f(0)∈A}的ACCP条件和BFD性质.结果表明,整环{f∈[[BS,≤]]|f(0)∈A}的分解性质不仅依赖于A和B的分解性质以及U(A)和U(B),而且还依赖于幺半群S的分解性质.该结果能够构造出具有某种分解性质的整环的新例子. 相似文献
2.
刘仲奎 《数学年刊A辑(中文版)》2005,(5)
设A■B是整环的扩张, (S,≤)是满足一定条件的严格偏序幺半群, [[BS,≤]]是整环B上的广义幂级数环.本文研究整环[[BS,≤]]和{f∈[[BS,≤]]|f(0)∈A}的ACCP条件和BFD性质. 结果表明,整环{f∈[[BS,≤]]|f(0)∈A}的分解性质不仅依赖于A和B的分解性质以及U(A)和U(B),而且还依赖于幺半群S的分解性质.该结果能够构造出具有某种分解性质的整环的新例子. 相似文献
3.
广义幂级数环的Morita对偶 总被引:1,自引:0,他引:1
设A,B是有单位元的环, (S,≤)是有限生成的Artin的严格全序幺半群, AMB是双模.本文证明了双模[[AS,≤]][MS,≤][[BS,≤]]定义一个Morita对偶当且仅当 AMB定义一个Morita对偶且A是左noether的,B是右noether的.因此A上的广 义幂级数环[[AS,≤]]具有Morita对偶当且仅当A是左noether的且具有由双模AMB 诱导的Morita对偶,使得B是右noether的. 相似文献
4.
作为幂级数环的推广,Ribenboim引入了广义幂级数环的概念.设R是有单位元的交换环,(J,≤)是严格全序半群.本文中我们证明了如下结果:(1)广义幂级数环 [[Rs]]是PP-环当且仅当R是PP-环且B(R)的任意 S-可标子集C在B(R)中有最小上界;(2)如果对任意s∈S都有0≤s,则[[Rs,≤]]是弱PP-环当且仅当R是弱PP-环.我们还给出了一个例子说明交换的弱PP-环可以不是PP-环. 相似文献
5.
本文研究了广义幂级数环与其系数环在本质理想和非奇异性上的关系.利用本质理想的定义和性质,得到了广义幂级数环的左理想为本质左理想的菪干充分必要条件.在此基础上,给出了广义幂级数环为左非奇异环的充分必要条件. 相似文献
6.
广义幂级数环的拟Baer性 总被引:3,自引:0,他引:3
设R是环,(S,≤)是严格全序幺半群,且对任意s∈S都有0≤s.本文证明了环R是拟Baer环当且仅当R上的广义幂级数环[RS,≤]]是拟Baer环。 相似文献
7.
刘仲奎 《数学年刊A辑(中文版)》2002,(5)
设R是环,(S,≤)是严格全序幺半群,且对任意s∈S都有0≤s.本文证明了环R是拟Baer环当且仅当R上的广义幂级数环[[RS,≤]]是拟 Baer环. 相似文献
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9.
设R是有单位元1的结合环,(S,≤)是严格全序Artin幺半群,M_R是右R-模,Att(M_R)与Att([M~(S,≤)]_([[R~(S,≤)]]))分别表示模M_R与广义逆多项式模[M~(S,≤)]_([[R~(S,≤)]])的所有Attached素理想组成的集合.该文主要讨论了广义幂级数环[[R~(S;≤)]]广义逆多项式模[[R~(S;≤)]]的Attached素理想的相关性质,证明了在一定条件下,有Att([M~(S,≤)]_([[R~(S,≤)]])={[[PR~(S;≤)]]P∈Att(M_R)}.这一结论表明广义逆多项式模([M~(S,≤)]_([[R~(S,≤)]])的Attached素理想在一定条件下可以用模M_R的Attached素理想来刻画,推广了Annin S在文献[1]中关于斜多项式环上逆多项式模的Attached素理想的相关结论. 相似文献
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Zhong Kui Liu 《数学学报(英文版)》2002,18(2):245-252
Let A, B be associative rings with identity, and (S, ≤) a strictly totally ordered monoid which is also artinian and finitely generated. For any bimodule
A
M
B
, we show that the bimodule [[
AS,≤
]][M
S
,≤][[
BS, ≤
]] defines a Morita duality if and only if
A
M
B
defines a Morita duality and A is left noetherian, B is right noetherian. As a corollary, it is shown that the ring [[A
S
,≤]] of generalized power series over A has a Morita duality if and only if A is a left noetherian ring with a Morita duality induced by a bimodule
A
M
B
such that B is right noetherian.
Received April 13, 1999, Accepted December 12, 1999 相似文献
12.
A. Majidinya 《代数通讯》2013,41(4):1460-1472
Let R be a ring and S a strictly totally ordered monoid. Let ω: S → End(R) be a monoid homomorphism. Let M R be an ω-compatible module and either R satisfies the ascending chain conditions (ACC) on left annihilator ideals or every S-indexed subset of right semicentral idempotents in R has a generalized S-indexed join. We show that M R is p.q.-Baer if and only if the generalized power series module M[[S]] R[[S, ω]] is p.q.-Baer. As a consequence, we deduce that for an ω-compatible ring R, the skew generalized power series ring R[[S, ω]] is right p.q.-Baer if and only if R is right p.q.-Baer and either R satisfies the ACC on left annihilator ideals or any S-indexed subset of right semicentral idempotents in R has a generalized S-indexed join in R. Examples to illustrate and delimit the theory are provided. 相似文献
13.
Let R be a ring and (S, 〈) be a strictly totally ordered monoid satisfying that 0 〈 s for all s C S. It is shown that if A is a weakly rigid homomorphism, then the skew generalized power series ring [[RS,-〈, λ]] is right p.q.-Baer if and only if R is right p.q.-Baer and any S-indexed subset of S,(R) has a generalized join in S,(R). Several known results follow as consequences of our results. 相似文献
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15.
Zhong Kui LIU 《数学学报(英文版)》2006,22(4):989-998
Let R be a ring and S a cancellative and torsion-free monoid and 〈 a strict order on S. If either (S,≤) satisfies the condition that 0 ≤ s for all s ∈ S, or R is reduced, then the ring [[R^S,≤]] of the generalized power series with coefficients in R and exponents in S has the same triangulating dimension as R. Furthermore, if R is a PWP ring, then so is [[R^S,≤]]. 相似文献
16.
In this paper we introduce a construction called the skew generalized power series ring R[[S, ω]] with coefficients in a ring R and exponents in a strictly ordered monoid S which extends Ribenboim's construction of generalized power series rings. In the case when S is totally ordered or commutative aperiodic, and ω(s) is constant on idempotents for some s ∈ S?{1}, we give sufficient and necessary conditions on R and S such that the ring R[[S, ω]] is von Neumann regular, and we show that the von Neumann regularity of the ring R[[S, ω]] is equivalent to its semisimplicity. We also give a characterization of the strong regularity of the ring R[[S, ω]]. 相似文献
17.
Let R be a ring, (S, ≤) a strictly ordered monoid and ω: S → End(R) a monoid homomorphism. The skew generalized power series ring R[[S, ω]] is a common generalization of (skew) polynomial rings, (skew) power series rings, (skew) Laurent polynomial rings, (skew) group rings, and Mal'cev–Neumann Laurent series rings. In this article, we study relations between the (quasi-) Baer, principally quasi-Baer and principally projective properties of a ring R, and its skew generalized power series extension R[[S, ω]]. As particular cases of our general results, we obtain new theorems on (skew) group rings, Mal'cev–Neumann Laurent series rings, and the ring of generalized power series. 相似文献
18.
In this paper, we show that if rings A and B are (s, 2)-rings, then so is the ring of a Morita Context([[A^S,≤]],[[B^S,≤]],[[M^S,≤]],[[N^S,≤]],ψ^S,Ф^S)of generalized power series. Also we get analogous results for unit 1-stable ranges, GM-rings and rings which have stable range one. These give new classes of rings satisfying such stable range conditions. 相似文献
19.
Let R be a ring, S a strictly ordered monoid, and ω: S → End(R) a monoid homomorphism. In [30], Marks, Mazurek, and Ziembowski study the (S, ω)-Armendariz condition on R, a generalization of the standard Armendariz condition from polynomials to skew generalized power series. Following [30], we provide various classes of nonreduced (S, ω)-Armendariz rings, and determine radicals of the skew generalized power series ring R[[S ≤, ω]], in terms of those of an (S, ω)-Armendariz ring R. We also obtain some characterizations for a skew generalized power series ring to be local, semilocal, clean, exchange, uniquely clean, 2-primal, or symmetric. 相似文献