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Orthodox semigroups whose idempotents satisfy a certain identity

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Abstract

An orthodox semigroup S is called a left [right] inverse semigroup if the set of idempotents of S satisfies the identity xyx=xy [xyx=yx]. Bisimple left [right] inverse semigroups have been studied by Venkatesan [6]. In this paper, we clarify the structure of general left [right] inverse semigroups. Further, we also investigate the structure of orthodox semigroups whose idempotents satisfy the identity xyxzx=xyzx. In particular, it is shown that the set of idempotents of an orthodox semigroup S satisfies xyxzx=xyzx if and only if S is isomorphic to a subdirect product of a left inverse semigroup and a right inverse semigroup.

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  1. Shimane University, Matsue, Shimane, Japan

    Miyuki Yamada

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  1. Miyuki Yamada
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Communicated by T. Saitô

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Yamada, M. Orthodox semigroups whose idempotents satisfy a certain identity. Semigroup Forum 6, 113–128 (1973). https://doi.org/10.1007/BF02389116

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  • DOI: https://doi.org/10.1007/BF02389116

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