Frontiers of Mathematics in China >

2017 , Vol. 12 >Issue 5: 1045 - 1056

DOI: https://doi.org/10.1007/s11464-017-0655-y

RESEARCH ARTICLE

Trivial extension of Koszul algebras

  • Zhi CHENG
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  • School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241002, China

Received date: 04 May 2017

Accepted date: 13 Jul 2017

Published date: 30 Sep 2017

Copyright

2017 Higher Education Press and Springer-Verlag GmbH Germany
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Abstract

Let Λ be a Koszul algebra, and let Mbe a graded Λ-bimodule. We prove that the trivial extension algebra of Λ by Mis also a Koszul algebra whenever Mis Koszul as a left Λ-module. Applications and examples are also provided.

Key words： Koszul algebra; Koszul module; trivial extension

Cite this article

Zhi CHENG . Trivial extension of Koszul algebras[J]. Frontiers of Mathematics in China, 2017 , 12(5) : 1045 -1056 . DOI: 10.1007/s11464-017-0655-y

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