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<p>For each of the following conditions, we characterize the pseudovarieties of semigroups <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\textsf{V}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="sans-serif">V</mi> </math></EquationSource> </InlineEquation> that satisfy it: (i) every epimorphism to a member of&#xa0;<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\textsf{V}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="sans-serif">V</mi> </math></EquationSource> </InlineEquation> is onto; (ii) every epimorphism to a finite semigroup with domain a member of&#xa0;<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\textsf{V}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="sans-serif">V</mi> </math></EquationSource> </InlineEquation> is onto; (iii) for every epimorphism <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(S\rightarrow T\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>S</mi> <mo stretchy="false">→</mo> <mi>T</mi> </mrow> </math></EquationSource> </InlineEquation> with <i>S</i> in&#xa0;<InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\textsf{V}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="sans-serif">V</mi> </math></EquationSource> </InlineEquation> and <i>T</i> finite, <i>T</i> is also a member of&#xa0;<InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\textsf{V}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="sans-serif">V</mi> </math></EquationSource> </InlineEquation>.</p>

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Epimorphisms and pseudovarieties of semigroups

  • 期刊论文

  • 发表日期：

    2025年11月24日

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  • Jorge Almeida,
  • Aftab Hussain Shah

摘要

For each of the following conditions, we characterize the pseudovarieties of semigroups \(\textsf{V}\) V that satisfy it: (i) every epimorphism to a member of  \(\textsf{V}\) V is onto; (ii) every epimorphism to a finite semigroup with domain a member of  \(\textsf{V}\) V is onto; (iii) for every epimorphism \(S\rightarrow T\) S → T with S in  \(\textsf{V}\) V and T finite, T is also a member of  \(\textsf{V}\) V .