Epis from locally inverse semigroups are onto (Q1905972)
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scientific article; zbMATH DE number 836807
| Language | Label | Description | Also known as |
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| English | Epis from locally inverse semigroups are onto |
scientific article; zbMATH DE number 836807 |
Statements
Epis from locally inverse semigroups are onto (English)
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30 June 1996
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In the previous paper of the author [Semigroup Forum 23, 255-259 (1981; Zbl 0475.20052)], it was proved that, within the category of semigroups, any epimorphism from a generalized inverse semigroup is onto. The class of generalized inverse semigroups is equal to the class of orthodox locally inverse semigroups [see \textit{M. Yamada}, Pac. J. Math. 21, 371-392 (1967; Zbl 0154.01603)]. In general, orthodox semigroups have non-surjective epimorphisms. In this paper, the author shows that any epimorphism from a locally inverse semigroup is onto. The author's proof is based on \textit{J. R. Isbell}'s Zigzag Theorem [Proc. Conf. Categorical Algebra, La Jolla 1965, 232-246 (1966; Zbl 0194.01601)].
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Isbell's zigzag theorem
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category of semigroups
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generalized inverse semigroups
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locally inverse semigroups
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epimorphisms
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0.8017957210540771
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0.7288877367973328
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0.7250481247901917
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