共查询到20条相似文献,搜索用时 83 毫秒
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Dn型路代数本性倾斜模的一个必要条件 总被引:1,自引:1,他引:0
倾斜理论是研究代数表示理论的重要工具之一.本文主要对Dn(n≥4),E6,E7,E8型路代数倾斜模在其对应的AR-箭图上的结构持点进行研究.通过对Dn(n≥4),上E6,E7,E8型路代数A的AR-箭图ΓA分析证明了Dn≥4),E6,E7,E8型路代数本性慨斜模TA的一个必要条件是:在A的AR-箭图ΓA的每个边缘的r-轨道都有TA的不可分解直和项对应的点. 相似文献
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证明同调有界的连通微分分次代数(简称为DG代数)上的紧致DG模的ampli-tude与基代数的amplitude的差恰为该DG模的投射维数.由此可得非平凡的正则DG代数是同调无界的.对正则DG代数A,若它的同调代数H(A)是分次Koszul代数,则证明H(A)有有限的整体维数;如果把条件减弱为A是Koszul DG代数,则给出了一个H(A)的整体维数为无限的例子.对一般的正则DG代数A,给出了其为Gorenstein DG代数的一些等价刻画.对同调有限维的连通DG代数A,证明由紧致对象全体构成的三角范畴Dc(A)和Dc(Aop)存在Auslander-Reiten三角当且仅当A和Aop都是Gorenstein DG代数.当A是非平凡的正则DG代数,且H(A)是局部有限维时,Dc(A)不存在Auslander-Reiten三角.对正则DG代数A,转而讨论了Auslander-Reiten三角在Dlbf(A)以及Dlbf(Aop)上的存在性. 相似文献
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本文给出K—代数A上一种较为广泛的阶法子,在此滤子下运用Groebner基理论,给出了A和两个分次代数grC(A)与(A^~)的关系。 相似文献
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该文依据弱Hopf代数的定义给出弱Hopf超代数的定义.进而利用弱反极取代Hopf代数中反极的方法,构造一类不是Hopf超代数的弱Hopf超代数wslq^d(m|n),并给出了wslq^d(m|n)的PBW基. 相似文献
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张顺华 《数学物理学报(A辑)》1998,(1)
设A是有限域上的型的遗传代数,(A)和C(A)分别表示A的Ringel-Hall代数和合成代数.该文证明了C(A)=其中和分别表示由预投射模和预内射模生成的子代数,是由C(A)中的正则元素生成的子代数. 相似文献
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陈露 《纯粹数学与应用数学》2011,27(4):433-436
为了深入研究N(2,2,0)代数的代数结构,在N(2,2,0)代数中建立了中间幂等元的概念,讨论了它的基本性质,给出了中间幂等元关联的集合坞是(S,*,△,0)的子代数的一个条件.证明了当U(2,2,0)代数中包含一个右零半群时,Mg是幂等元集E(S)的子集.并利用坞定义了一个等价关系. 相似文献
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谭绍滨 《数学年刊A辑(中文版)》2002,(3)
本文将Kac-Moody代数A1(1)的二阶表示理论[11]推广到Toroidal李代数的情形.并给出了A1型Toroidal李代数的一类不可约表示. 相似文献
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For a monoid M, we introduce the concept of skew strongly M-reversible rings which is a generalization of strongly M-reversible rings, and investigate their properties. It is shown that if G is a finitely generated Abelian group, then G is torsion-free if and only if there exists a ring R with |R| ≥ 2 such that R is skew strongly G-reversible. Moreover, we prove that if R is a right Ore ring with classical right quotient ring Q, then R is skew strongly M-reversible if and only if Q is skew strongly M-reversible. 相似文献
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In this work, free multivariate skew polynomial rings are considered, together with their quotients over ideals of skew polynomials that vanish at every point (which includes minimal multivariate skew polynomial rings). We provide a full classification of such multivariate skew polynomial rings (free or not) over finite fields. To that end, we first show that all ring morphisms from the field to the ring of square matrices are diagonalizable, and that the corresponding derivations are all inner derivations. Secondly, we show that all such multivariate skew polynomial rings over finite fields are isomorphic as algebras to a multivariate skew polynomial ring whose ring morphism from the field to the ring of square matrices is diagonal, and whose derivation is the zero derivation. Furthermore, we prove that two such representations only differ in a permutation on the field automorphisms appearing in the corresponding diagonal. The algebra isomorphisms are given by affine transformations of variables and preserve evaluations and degrees. In addition, ours proofs show that the simplified form of multivariate skew polynomial rings can be found computationally and explicitly. 相似文献
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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 paper we obtain necessary and sufficient conditions for the skew generalized power series ring R[[S,ω]] to be a semiprime, prime, quasi-Baer, or Baer ring. Furthermore, we study the prime radical of a skew generalized power series ring R[[S,ω]]. Our results extend and unify many existing results. In particular, 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
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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
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Let α be a nonzero endomorphism of a ring R, n be a positive integer and T_n(R, α) be the skew triangular matrix ring. We show that some properties related to nilpotent elements of R are inherited by T_n(R, α). Meanwhile, we determine the strongly prime radical, generalized prime radical and Behrens radical of the ring R[x; α]/(x~n), where R[x; α] is the skew polynomial ring. 相似文献
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In this paper, a sufficient condition is given under which the smash product A#H is a transfinite left free normalizing extension of an algebra A. Moreover, the result is applied to a skew semigroup ring, a skew group ring and the quantum group U
q
(sl(2)) such that some properties are shown.
Received April 14, 1997, Accepted August 10, 1998 相似文献
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本文中对一个斜群环为Dubrovin赋值环给出了一系列等价刻画,并且刻画了一个Dubrovin赋值斜群环的所有素理想. 相似文献
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Let α be an automorphism of a ring R. We study the skew Armendariz of Laurent series type rings (α-LA rings), as a generalization of the standard Armendariz condition from polynomials to skew Laurent series. We study on the relationship between the Baerness and p.p. property of a ring R and these of the skew Laurent series ring R[[x, x ?1; α]], in case R is an α-LA ring. Moreover, we prove that for an α-weakly rigid ring R, R[[x, 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 α-LA rings are provided. 相似文献
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Chan Yong HONG Nam Kyun KIM Tai Keun KWAK Yang LEE 《Frontiers of Mathematics in China》2016,11(4):869-900
We study structures of Hochschild 2-cocycles related to endomorphisms and introduce a skew Hochschild 2-cocycle. We moreover define skew Hochschild extensions equipped with skew Hochschild 2-cocycles, and then we examine uniquely clean, Abelian, directly finite, symmetric, and reversible ring properties of skew Hochschild extensions and related ring systems. The results obtained here provide various kinds of examples of such rings. Especially, we give an answer negatively to the question of H. Lin and C. Xi for the corresponding Hochschild extensions of reversible (or semicommutative) rings. Finally, we establish three kinds of Hochschild extensions with Hochschild 2-cocycles and skew Hochschild 2-cocycles. 相似文献