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<p>In this note, we first indicate that any 0-inversive semigroup with a least non-zero idempotent has no proper divisors of 0. Moreover, we introduce the notion of a homo-left-group and generalize a variety of results of Mitsch and Petrich. These obtained statements seem to be new even for the class of all regular and finite semigroups.</p>

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Some remarks on a paper by Mitsch and Petrich

  • 期刊论文

  • 发表日期：

    2025年1月21日

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  • Roman S. Gigoń

摘要

In this note, we first indicate that any 0-inversive semigroup with a least non-zero idempotent has no proper divisors of 0. Moreover, we introduce the notion of a homo-left-group and generalize a variety of results of Mitsch and Petrich. These obtained statements seem to be new even for the class of all regular and finite semigroups.