Abstract
Let H = M0(G; I, Λ; P) be a Rees semigroup of matrix type with sandwich matrix P over a group H0 with zero. If F is a subgroup of G of finite index and X is a system of representatives of the left cosets of F in G, then with the matrix P there is associated in a natural way a matrix P(F, X) over the group F0 with zero. Our main result: the semigroup algebra K[H] of H over a field K of characteristic 0 satisfies an identity if and only if G has an Abelian subgroup F of finite index and, for any X, the matrix P(F, X) has finite determinant rank.
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Translated from Matematicheskie Zametki, Vol. 18, No. 2, pp. 203–212, August, 1975.
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Domanov, O.I. Identities of semigroup algebras of completely O-simple semigroups. Mathematical Notes of the Academy of Sciences of the USSR 18, 707–712 (1975). https://doi.org/10.1007/BF01818036
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DOI: https://doi.org/10.1007/BF01818036