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We introduce a generalization of the notion of a Koszul algebra, which includes graded algebras with relations in different
degrees, and we establish some of the basic properties of these algebras. This class is closed under twists, twisted tensor
products, regular central extensions and Ore extensions. We explore the monomial algebras in this class and we include some
well-known examples of algebras that fall into this class. 相似文献
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Christopher Phan 《代数通讯》2013,41(3):834-844
Let A be a connected-graded algebra with trivial module 𝕜, and let B be a graded Ore extension of A. We relate the structure of the Yoneda algebra E(A): = Ext A (𝕜, 𝕜) to E(B). Cassidy and Shelton have shown that when A satisfies their 𝒦2 property, B will also be 𝒦2. We prove the converse of this result. 相似文献
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Ayako Itaba 《代数通讯》2013,41(1):404-415
We calculate the dimensions of the Hochschild cohomology groups of a self-injective special biserial algebra Λ s obtained by a circular quiver with double arrows. Moreover, we give a presentation of the Hochschild cohomology ring modulo nilpotence of Λ s by generators and relations. This result shows that the Hochschild cohomology ring modulo nilpotence of Λ s is finitely generated as an algebra. 相似文献
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Sandra Mara Alves Jorge 《代数通讯》2013,41(6):2184-2198
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The Maximal Graded Left Quotient Algebra of a Graded Algebra1) 总被引:1,自引:0,他引:1
Gonzalo ARANDA PINO Mercedes SILES MOLINA 《数学学报(英文版)》2006,22(1):261-270
We construct the maximal graded left quotient algebra of every graded algebra A without homogeneous total right zero divisors as the direct limit of graded homomorphisms (of left A-modules) from graded dense left ideals of A into a graded left quotient algebra of A. In the case of a superalgebra, and with some extra hypothesis, we prove that the component in the neutral element of the group of the maximal graded left quotient algebra coincides with the maximal left quotient algebra of the component in the neutral element of the group of the superalgebra. 相似文献
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In this paper, we establish some new Foxby equivalences between some Gorenstein subcategories in the Auslander class 𝒜C(R) and that in the Bass class ?C(S) in a general setting. Our results provide a unification and generalization of some known results and generate some new Foxby equivalences of categories. 相似文献
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We introduce the notion of 𝒦-nonsingularity of a module and show that the class of 𝒦-nonsingular modules properly contains the classes of nonsingular modules and of polyform modules. A necessary and sufficient condition is provided to ensure that this property is preserved under direct sums. Connections of 𝒦-nonsingular modules to their endomorphism rings are investigated. Rings for which all modules are 𝒦-nonsingular are precisely determined. Applications include a type theory decomposition for 𝒦-nonsingular extending modules and internal characterizations for 𝒦-nonsingular continuous modules which are of type I, type II, and type III, respectively. 相似文献
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In this paper, the concept of the ??-constructibility of graphs is introduced and investigated with particular reference to planar graphs. It is conjectured that the planar graphs are minimally N-constructible, where N is a finite set of graphs and an infinite set ?? is obtained such that the planar graphs are also minimally ??-constructible. Finally, some properties of the set of all N-constructible graphs are discussed and compared with the corresponding properties of planar graphs. 相似文献
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《代数通讯》2013,41(7):2219-2229
ABSTRACT In this article, we focus on the result of V.F.R. Jones which says that the partition algebra is the algebra of all transformations commuting with the action of the symmetric group on tensor products of its permutation representation. In particular, we restrict the action of the symmetric group to the action of the alternating group. In this context, we compute a basis for the centralizer algebra and show when the centralizer is isomorphic to the partition algebra. 相似文献
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Donald W. Barnes 《代数通讯》2013,41(4):1170-1171
Let 𝔉 be a saturated formation of soluble Lie algebras. Let L be a soluble Lie algebra, and let U be an 𝔉-normalizer of L. Then U is intravariant in L. 相似文献
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Fabrizio Zanello 《代数通讯》2013,41(4):1087-1091
The purpose of this note is to supply an upper and a lower bound (which are in general sharp) for the h-vector of a level algebra which is relatively compressed with respect to any arbitrary level algebra A. The useful concept of relatively compressed algebra was recently introduced in Migliore et al. (2005) (whose investigations mainly focused on the particular case of A a complete intersection). The key idea of this note is the simple observation that the level algebras which are relatively compressed with respect to A coincide (after an obvious isomorphism) with the generic level quotients of suitable truncations of A. Therefore, we are able to apply to relatively compressed algebras the main result of our recent work, Zanello (2007). 相似文献
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Let R be a ring and 𝒲 a self-orthogonal class of left R-modules which is closed under finite direct sums and direct summands. A complex C of left R-modules is called a 𝒲-complex if it is exact with each cycle Z n (C) ∈ 𝒲. The class of such complexes is denoted by 𝒞𝒲. A complex C is called completely 𝒲-resolved if there exists an exact sequence of complexes D · = … → D ?1 → D 0 → D 1 → … with each term D i in 𝒞𝒲 such that C = ker(D 0 → D 1) and D · is both Hom(𝒞𝒲, ?) and Hom(?, 𝒞𝒲) exact. In this article, we show that C = … → C ?1 → C 0 → C 1 → … is a completely 𝒲-resolved complex if and only if C n is a completely 𝒲-resolved module for all n ∈ ?. Some known results are obtained as corollaries. 相似文献
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文献[1]从Euclid空间R^v(v≥1)的一个半格S出发,定义了一个Jordan代数J(S):然后通过Tits—Kantor-Koecher方法由J(S)构造出Lie代数G(J(S)).最后利用G(J(S))得到A1型扩张仿射Lie代数L(J(S)).本文给出v=2,S为格时。A1型扩张仿射Lie代数L(J(S))的Z^2一分次自同构群. 相似文献