摘要 :
The Koszul-like property for any finitely generated graded modules over a Koszul-like algebra is investigated and the notion of weakly Koszul-like module is introduced. We show that a finitely generated graded module M is a weakly...
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The Koszul-like property for any finitely generated graded modules over a Koszul-like algebra is investigated and the notion of weakly Koszul-like module is introduced. We show that a finitely generated graded module M is a weakly Koszul-like module if and only if it can be approximated by Koszul-like graded submodules, which is equivalent to the fact that G(M) is a Koszul-like module, where G(M) denotes the associated graded module of M. As applications, the relationships between minimal graded projective resolutions of M and G(M), and Koszul-like submodules are established. Moreover, the Koszul dual of a weakly Koszul-like module is proved to be generated in degree 0 as a graded E(A) -module.
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摘要 :
In this paper, the notion of Koszul-like algebra is introduced; this notion generalizes the notion of Koszul algebra and includes some Artin-Schelter regular algebras of global dimension 5 as special examples. Basic properties of ...
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In this paper, the notion of Koszul-like algebra is introduced; this notion generalizes the notion of Koszul algebra and includes some Artin-Schelter regular algebras of global dimension 5 as special examples. Basic properties of Koszul-like modules are discussed. In particular, some necessary and sufficient conditions for ΚL(A) = L(A) are provided, where ΚL(A) and L(A) denote the categories of Koszul-like modules and modules with linear presentations (see [1]-[3], etc.) respectively, and A is a Koszul-like algebra. We construct new Koszul-like algebras from the known ones by the "one-point extension." Some criteria for a graded algebra to be Koszul-like are provided. Finally, we construct many classical Koszul objects from the given Koszul-like objects.
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摘要 :
The so-called λ-Koszul algebra and λ-Koszul module are introduced. We give different equivalent descriptions of the λ-Koszul algebra in terms of its minimal graded projective resolution and the Yoneda Ext-algebra E(A) = ⊕_(i≥...
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The so-called λ-Koszul algebra and λ-Koszul module are introduced. We give different equivalent descriptions of the λ-Koszul algebra in terms of its minimal graded projective resolution and the Yoneda Ext-algebra E(A) = ⊕_(i≥0)Ext_A~iF,F). The "λ-Koszulity" of a finitely generated graded module is discussed and the concepts of (strongly) weakly λ-Koszul module are introduced. Finally, we discuss the A_∞-structure on the Yoneda Ext-algebra of a λ-Koszul algebra.
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