共查询到10条相似文献,搜索用时 93 毫秒
1.
We study the skew inverse Laurent-serieswise Armendariz (or simply, SIL-Armendariz) condition on R, a generalization of the standard Armendariz condition from polynomials to skew inverse Laurent series. We study relations between the set of annihilators in R and the set of annihilators in R((x ?1; α)). Among applications, we show that a number of interesting properties of a SIL-Armendariz ring R such as the Baer and the α-quasi Baer property transfer to its skew inverse Laurent series extensions R((x ?1; α)) and vice versa. For an α-weakly rigid ring R, R((x ?1; α)) is a left p.q.-Baer ring if and only if R is left p.q.-Baer and every countable subset of S ?(R) has a generalized countable join in R. Various types of examples of SIL-Armendariz rings is provided. 相似文献
2.
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
3.
For a ring endomorphism α, we introduce and investigate SPA-rings which are a generalization of α-rigid rings and determine the radicals of the skew polynomial rings R[x; α], R[x, x ?1; α] and the skew power series rings R[[x; α]], R[[x, x ?1; α]], in terms of those of R. We prove that several properties transfer between R and the extensions, in case R is an SPA-ring. We will construct various types of nonreduced SPA-rings and show SPA is a strictly stronger condition than α-rigid. 相似文献
4.
Miao-Sen Chen 《Southeast Asian Bulletin of Mathematics》2000,24(1):25-29
In this paper, we shall discuss the conditions for a right SC right CS ring to be a QF ring. In particular, we prove that if R is a right SI right CS ring satisfying the reflexive orthogonal condition (*) and if every CS right R-module is -CS, then R is a QF ring.AMS Subject Classification (1991): 16L30 16L60 相似文献
5.
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
6.
Abdollah Alhevaz 《代数通讯》2017,45(3):919-923
Ever since the introduction, skew inverse Laurent series rings have kept growing in importance, as researchers characterized their properties (such as Noetherianness, Armendarizness, McCoyness, etc.) in terms of intrinsic properties of the base ring and studied their relations with other fields of mathematics, as for example quantum mechanics theory. The goal of our paper is to study the primeness and semiprimeness of general skew inverse Laurent series rings R((x?1;σ,δ)), where R is an associative ring equipped with an automorphism σ and a σ-derivation δ. 相似文献
7.
Let α be an endomorphism of R which is not assumed to be surjective and R be α-compatible. It is shown that the skew power series ring R[[x; α]] is right p.q.-Baer if and only if the skew Laurent series ring R[[x, x ?1; α]] is right p.q.-Baer if and only if R is right p.q.-Baer and every countable subset of right semicentral idempotents has a generalized countable join. Examples to illustrate and delimit the theory are provided. 相似文献
8.
A right R-module M is called glat if any homomorphism from any finitely presented right R-module to M factors through a finitely presented Gorenstein projective right R-module. The concept of glat modules may be viewed as another Gorenstein analogue of flat modules. We first prove that the class of glat right R-modules is closed under direct sums, direct limits, pure quotients and pure submodules for arbitrary ring R. Then we obtain that a right R-module M is glat if and only if M is a direct limit of finitely presented Gorenstein projective right R-modules. In addition, we explore the relationships between glat modules and Gorenstein flat (Gorenstein projective) modules. Finally we investigate the existence of preenvelopes and precovers by glat and finitely presented Gorenstein projective modules. 相似文献
9.
10.
A. R. Nasr-Isfahani 《代数通讯》2013,41(3):1337-1349
In this note we study radicals of skew polynomial ring R[x; α] and skew Laurent polynomial ring R[x, x ?1; α], for a skew-Armendariz ring R. In particular, among the other results, we show that for an skew-Armendariz ring R, J(R[x; α]) = N 0(R[x; α]) = Ni?*(R)[x; α] and J(R[x, x ?1; α]) = N 0(R[x, x ?1; α]) = Ni?*(R)[x, x ?1; α]. 相似文献