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1.
Robert L. Snider 《Proceedings of the American Mathematical Society》1996,124(4):1043-1049
If is a finitely generated nilpotent group which is not abelian-by-finite, a field, and a finite dimensional separable division algebra over , then there exists a simple module for the group ring with endomorphism ring . An example is given to show that this cannot be extended to polycyclic groups.
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3.
We will show that skew polynomial rings in several variables over locally nilpotent rings cannot contain nonzero idempotent elements. We will also prove that such rings are Brown–McCoy radical. 相似文献
4.
A. A. Tuganbaev 《Mathematical Notes》1999,65(6):739-748
This paper continues the study of Noetherian serial rings. General theorems describing the structure of such rings are proved.
In particular, some results concerning π-projective and π-injective modules over serial rings are obtained.
Translated fromMatematicheskie Zametki, Vol. 65, No. 6, pp. 880–892 June, 1999. 相似文献
5.
Huanyin Chen 《Czechoslovak Mathematical Journal》2008,58(2):417-428
An exchange ring R is strongly separative provided that for all finitely generated projective right R-modules A and B, A ⊕ A ≅ A ⊕ B ⇒ A ≅ B. We prove that an exchange ring R is strongly separative if and only if for any corner S of R, aS + bS = S implies that there exist u, v ∈ S such that au = bv and Su + Sv = S if and only if for any corner S of R, aS + bS = S implies that there exists a right invertible matrix ∈ M
2(S). The dual assertions are also proved. 相似文献
6.
Let R be an hereditary Noetherian prime ring (or, HNP-ring, for short), and let S?=?R[x;σ] be a skew polynomial ring over R with σ being an automorphism on R. The aim of the paper is to describe completely the structure of right projective ideals of R[x;σ] where R is an HNP-ring and to obtain that any right projective ideal of S is of the form X𝔟[x;σ], where X is an invertible ideal of S and 𝔟 is a σ-invariant eventually idempotent ideal of R. 相似文献
7.
Marjan Sheibani Abdolyousefi 《代数通讯》2018,46(4):1527-1533
A ring R is Zhou nil-clean if every element in R is the sum of two tripotents and a nilpotent that commute. Let R be a Zhou nil-clean ring. If R is 2-primal (of bounded index), we prove that every square matrix over R is the sum of two tripotents and a nilpotent. These provide a large class of rings over which every square matrix has such decompositions by tripotent and nilpotent matrices. 相似文献
8.
Marjan Sheibani Abdolyousefi 《代数通讯》2017,45(5):1983-1995
A commutative ring R is J-stable provided that R∕aR has stable range 1 for all a?J(R). A commutative ring R in which every finitely generated ideal principal is called a Bézout ring. A ring R is an elementary divisor ring provided that every matrix over R admits a diagonal reduction. We prove that a J-stable ring is a Bézout ring if and only if it is an elementary divisor ring. Further, we prove that every J-stable ring is strongly completable. Various types of J-stable rings are provided. Many known results are thereby generalized to much wider class of rings, e.g. [3, Theorem 8], [4, Theorem 4.1], [7, Theorem 3.7], [8, Theorem], [9, Theorem 2.1], [14, Theorem 1] and [18, Theorem 7]. 相似文献
9.
The purpose of this paper is to study codes over finite principal ideal rings. To do this, we begin with codes over finite
chain rings as a natural generalization of codes over Galois rings GR(p
e
, l) (including ). We give sufficient conditions on the existence of MDS codes over finite chain rings and on the existence of self-dual codes
over finite chain rings. We also construct MDS self-dual codes over Galois rings GF(2
e
, l) of length n = 2
l
for any a ≥ 1 and l ≥ 2. Torsion codes over residue fields of finite chain rings are introduced, and some of their properties are derived. Finally,
we describe MDS codes and self-dual codes over finite principal ideal rings by examining codes over their component chain
rings, via a generalized Chinese remainder theorem.
相似文献
10.
设R′是一个环,Mn′(R′)是R′上的n′×n′矩阵环.如果环R有不变基数性质并且每个有限生成的投射左R-模是自由模,则R是一个投射自由环.如果环R≌Mr(S),其中S是一个投射自由环,则R是一个投射可迁环.当R是一个投射可迁环时,给出了从Mn′(R′)到Mn(R)(n′≥n≥2)的若当同态的代数公式. 相似文献
11.
Weakly regular modules over normal rings 总被引:1,自引:1,他引:0
A. N. Abyzov 《Siberian Mathematical Journal》2008,49(4):575-586
Under study are some conditions for the weakly regular modules to be closed under direct sums and the rings over which all modules are weakly regular. For an arbitrary right R-module M, we prove that every module in the category σ(M) is weakly regular if and only if each module in σ(M) is either semisimple or contains a nonzero M-injective submodule. We describe the normal rings over which all modules are weakly regular. 相似文献
12.
Mohamed Khalifa 《代数通讯》2017,45(8):3587-3593
Let R be a commutative ring with identity. We show that R[[X]] is strongly Hopfian bounded if and only if R has a strongly Hopfian bounded extension T such that Ic(T) contains a regular element of T. We deduce that if R[[X]] is strongly Hopfian bounded, then so is R[[X,Y]] where X,Y are two indeterminates over R. Also we show that if R is embeddable in a zero-dimensional strongly Hopfian bounded ring, then so is R[[X]] (this generalizes most results of Hizem [11]). For a chained ring R, we show that R[[X]] is strongly Hopfian if and only if R is strongly Hopfian. 相似文献
13.
We explore elementary matrix reduction over certain rings characterized by properties related to stable range. Let R be a commutative ring. We call R locally stable if aR+bR = R??x∈R such that R∕(a+bx)R has stable range 1. We study locally stable rings and prove that every locally stable Bézout ring is an elementary divisor ring. Many known results on domains are thereby generalized. 相似文献
14.
Huanyin Chen 《代数通讯》2013,41(9):4209-4216
It is shown that every exchange ring satisfying related comparability is separative. This yields that related comparability over exchange rings is Morita invariant. Also we investigate pseudosimilarity over exchange rings satisfying related comparability. 相似文献
15.
Wang Zhixi 《数学学报(英文版)》1997,13(4):513-516
The correlation between the resolution for a Zariskian filtered ringR and that for its associated graded ringG(R) is discussed in this note. Then we show some examples satisfying the condition of the theorem.
Project supported by NNSF of China and NSF of Beijing 相似文献
16.
Peter Symonds 《Advances in Mathematics》2007,208(1):408-421
Given a polynomial ring R over a field k and a finite group G, we consider a finitely generated graded RG-module S. We regard S as a kG-module and show that various conditions on S are equivalent, such as only containing finitely many isomorphism classes of indecomposable summands or satisfying a structure theorem in the sense of [D. Karagueuzian, P. Symonds, The module structure of a group action on a polynomial ring: A finiteness theorem, preprint, http://www.ma.umist.ac.uk/pas/preprints]. 相似文献
17.
Let R be a commutative, local, and principal ideal ring with maximal ideal and residue class field F. Suppose that every element of is square. Then the problem of classifying arbitrary symmetric matrices over R by congruence naturally reduces, and is actually equivalent to, the problem of classifying invertible symmetric matrices over F by congruence. 相似文献
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Sergei Evdokimov 《Journal of Combinatorial Theory, Series A》2010,117(7):827-841
It is proved that any Schur ring over a Galois ring of odd characteristic is either normal, or of rank 2, or a non-trivial generalized wreath product. The normal Schur rings are characterized as a special subclass of the cyclotomic Schur rings. 相似文献