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Vietnam Journal of Mathematics 34:3(2006) 341-351

 Weakly d-Koszul Modules

Jia-Feng Lu and Guo-Jun Wang

Abstract.  Let A be a d-Koszul algebra and M gr(A) we show that M is a weakly d-Koszul module if anf only if ε(G(M), A₀) = Extⁿ_A(M, A₀) is generated in degree 0 as a graded E(A) -module. Moreover, relations among weakly d-Koszul module, d-Koszul modules and Koszul modules are discussed. We also show that the Koszul dual of a weakly d-Koszul module M: ε(M) = Extⁿ_A(M, A₀) is finitely generated as a graded E(A)-module.

2000 Mathematics Subject Classification: 16E40, 14E45, 16S37, 16W50.

Keywords: $d$-Koszul algebras, $d$-Koszul modules, weakly $d$-Koszul modules.

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Published by Springer since January 2013