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Generalization of quasi-Koszul algebras. (English) Zbl 1224.16056

Summary: We generalize two kinds of graded algebras, \(\delta\)-Koszul algebras and \(\mathcal K_p\) algebras, to the non-graded cases. The trivial modules of \(\delta\)-Koszul algebras have pure resolutions, while those of \(\mathcal K_p\) algebras admit non-pure resolutions. We provide necessary and sufficient conditions for a Noetherian semiperfect algebra either to be a quasi-\(\delta\)-Koszul algebra or to be a quasi-\(\mathcal K_p\) algebra.

MSC:

16S37 Quadratic and Koszul algebras
16E05 Syzygies, resolutions, complexes in associative algebras
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References:

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