Medial permutable semigroups of the first kind |
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Authors: | Attila Nagy |
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Institution: | (1) Department of Algebra, Institute of Mathematics, Budapest University of Technology and Economics, Budapest, Hungary |
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Abstract: | We say that a semigroup S is a permutable semigroup if the congruences of S commute with each other, that is, α○β=β○α is satisfied for all congruences α and β of S. A semigroup is called a medial semigroup if it satisfies the identity axyb=ayxb. The medial permutable semigroups were examined in Proc. Coll. Math. Soc. János Bolyai, vol. 39, pp. 21–39 (1981), where the medial semigroups of the first, the second and the third kind were characterized, respectively. In Atta Accad.
Sci. Torino, I-Cl. Sci. Fis. Mat. Nat. 117, 355–368 (1983) a construction was given for medial permutable semigroups of the second the third] kind. In the present paper we give a
construction for medial permutable semigroups of the first kind. We prove that they can be obtained from non-archimedean commutative
permutable semigroups (which were characterized in Semigroup Forum 10, 55–66, 1975).
Research supported by the Hungarian NFSR grant No T042481 and No T043034. |
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Keywords: | Medial semigroups Right commutative and left commutative semigroups Permutable semigroups |
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