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<p>This article develops a theory of formations of completely simple semigroups, extending earlier work on inverse semigroups and orthodox semigroups. Firstly, we discuss the relation between the algebraic properties of a class of groups <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {G}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">G</mi> </math></EquationSource> </InlineEquation> and that of certain classes of completely simple semigroups with associated groups in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal {G}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">G</mi> </math></EquationSource> </InlineEquation>. Secondly, we prove that <i>i</i>-varieties of completely simple semigroups are closed under the product, while <i>f</i>-formations of completely simple semigroups are closed under the Gaschütz product, thereby extending corresponding results from group to semigroup theory.</p>

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Formations of completely simple semigroups

  • 期刊论文

  • 发表日期：

    2026年8月5日

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  • Minghui Li,
  • Dandan Yang

摘要

This article develops a theory of formations of completely simple semigroups, extending earlier work on inverse semigroups and orthodox semigroups. Firstly, we discuss the relation between the algebraic properties of a class of groups \(\mathcal {G}\) G and that of certain classes of completely simple semigroups with associated groups in \(\mathcal {G}\) G . Secondly, we prove that i-varieties of completely simple semigroups are closed under the product, while f-formations of completely simple semigroups are closed under the Gaschütz product, thereby extending corresponding results from group to semigroup theory.