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1.
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
2.
广义幂级数环上的PS模 总被引:1,自引:0,他引:1
Let R be a commutative ring and(S,≤)a strictly totally ordered monoid which satisfies the condition that 0≤s for every s ∈ S,In this paper we show that if RM is a PS-module,then the module [[M^s,≤]]of generalized power series over M is a PS [[R^s,≤]]-module. 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.
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
5.
《代数通讯》2013,41(8):3215-3226
Abstract Let R be a ring and (S, ≤) a strictly ordered monoid. Properties of the ring [[R S,≤]] of generalized power series with coefficients in R and exponents in S are considered in this paper. It is shown that [[R S,≤]] is reduced (2-primal, Dedekind finite, clean, uniquely clean) if and only if R is reduced (2-primal, Dedekind finite, clean, uniquely clean, respectively) under some additional conditions. Also a necessary and sufficient condition is given for rings under which the ring [[R S,≤]] is a reduced left PP-ring. 相似文献
6.
In this paper, we study the properties of generalized power series modules and the filtration dimensions of generalized power series algebras. We obtain that [[△S,≤]]- gfd([[AS,≤]]) =△-gfd(A) if A is an R-module where R is a perfect and coherent commutative algebra, and(R, ≤) is standardly stratified. 相似文献
7.
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
8.
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
9.
10.
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
11.
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
12.
We present two infinite families of generalized Lambert seriesidentities, and deduce several known identities from them. Theyinclude an identity due to M. Jackson, a corollary of Ramanujan's11-summation formula, and a recent identity of G. E. Andrews,R. P. Lewis and Z.-G. Liu. 2000 Mathematics Subject Classification33D15, 11D85. 相似文献
13.
本文给出了p—级数与广义积分∫10lnk-1x1-xdx,∫10lnk-1x1+xdx,∫10lnk-1x1-x2dx,∫10lnk-1x1+x2dx之间的关系.并通过一些p—级数的求和,给出了上述广义积分中某些积分的积分值. 相似文献
14.
Let R be an abelian ring. We consider a special subring An, relative to α2,…, αn∈ REnd(R), of the matrix ring Mn(R) over a ring R. It is shown that the ring An is a generalized right PP-ring (right zip ring) if and only if the ring R is a generalized right PP-ring (right zip ring). Our results yield more examples of generalized right PP-rings and right ziu rings. 相似文献
15.
In this article, we introduce a construction called the generalized inverse power series module M[[S ?1]] over a monoid ring R[S] with coefficients in an R-module M and exponents in a commutative monoid S. This construction is a generalization of the R[x]-modules which were discussed by S. Park in [12-14]. The injectivity and injective precovers of the generalized inverse power series module are considered. We also show that N is a pure submodule of M if and only if N[S] is a pure submodule of the monoid module M[S]. 相似文献
16.
17.
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
18.
I-Chiau Huang 《代数通讯》2013,41(7):2480-2498
A new notion of differentials is introduced to the method of generating functions for generalized power series with exponents in a totally ordered Abelian group. A logarithmic analogue of cohomology residues is defined to serve as a tool in the technique of equating coefficients. 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
20.
《代数通讯》2013,41(9):3305-3314
Abstract Let (S, ≤) be a strictly totally ordered monoid and R a domain. It is shown in this paper that [[R S,≤]], the ring of generalized power series with coefficients in R and exponents in S, satisfies the ascending chain condition for principal ideals if and only if the ring R and the monoid S satisfy the ascending chain condition for principal ideals of R, and of S, respectively. 相似文献