关于标准分层代数的多项式代数的滤链维数

标准分层代数是拟遗传代数的推广,其性质和理论意义受到人们的重视.在本文中,设A是域k上的标准分层代数,我们从特征模的角度,对A的多项式代数A[x]上的滤链维数进行了研究,得到了一些有意义的结果.     

广义幂级数环的Morita对偶

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.     

广义幂级数环上的PS模

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.     

广义幂级数环的PP性质

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．     

广义幂级数环的拟Baer性

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。     

广义幂级数环的拟Baer性

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.     

关于标准分层代数与它的多项式代数上的滤链维数

在本文中,我们研究了标准分层代数的Δ-好模滤链维数与它的多项式代数的Δ[x]-好模滤链维数,并得到了一些有趣的结果．     

广义逆多项式模的co-Hopf性质

设R是结合环(可以没有单位元),(S,≤)是严格全序幺半群,序≤是Artin的且对任意s∈S,有0≤s,则对任意具有性质(F)的左R-模M,[MS,≤]是co-Hopf左[[RS,≤]]一模当且仅当M是co-Hopf左R-模.     

Hausdorff维数和Packing维数

设W~(t)∶R N→Rd是N指标d维广义W inner过程,Bore l集E1,…,Em RN>.本文研究了在一定条件下,m项代数和W~(E1)W~(E2)…W~(Em)的H ausdorff维数和Pack ing维数的有关结论,其结果推广了文[3]的相关结果。     

广义路代数与点Hopf代数

Most of pointed Hopf algebras of dimension p^m with large coradtical are shown to be generalized path algebras. By the theory of generalized path algebras, the representations, homological dimensions and radicals of these Hopf algebras are obtained. The relations between the radicals of path algebras and connectivity of directed graphs are given.     

Principally Quasi-Baer skew Generalized Power Series modules

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.     

Morita Duality for the Rings of Generalized Power Series

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     

Triangular Matrix Representations of Rings of Generalized Power Series

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,≤]].     

PP-Rings of Generalized Power Series

Abstract As a generalization of power series rings, Ribenboim introduced the notion of the rings of generalized power series. Let R be a commutative ring, and (S, ≤) a strictly totally ordered monoid. We prove that (1) the ring [[R ^S,≤]] of generalized power series is a PP-ring if and only if R is a PP-ring and every S-indexed subset C of B(R) (the set of all idempotents of R) has a least upper bound in B(R) and (2) if (S, ≤) also satisfies the condition that 0 ≤s for any s∈S, then the ring [[R ^S,≤ ]] is weakly PP if and only if R is weakly PP. Research supported by National Natural Science Foundation of China, 19501007, and Natural Science Foundation of Gansu, ZQ-96-01