Abstract
We study Azumaya semigroup algebras and obtain a sufficient and necessary condition for the semigroup algebra of a finite semigroup to be Azumaya. In particular, we answer two problems of Okniński on Azumaya semigroup algebras, stated in his monograph (Semigroup Algebras, Marcel Dekker, New York, 1991).
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Acknowledgements
This research is supported by the National Natural Science Foundation of China (Grant: 11761034). The authors would like to thank the referees for their valuable comments and suggestions on the writing of this manuscript. Thanks go to Professor Okniński for his suggestions which refine the proofs of Lemma 3.3 and Theorem 3.4.
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Communicated by Jan Okniński.
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Guo, J., Guo, X. Semigroup algebras which are Azumaya algebras. Semigroup Forum 106, 160–168 (2023). https://doi.org/10.1007/s00233-023-10339-0
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DOI: https://doi.org/10.1007/s00233-023-10339-0