Epimorphisms, dominions and regular semigroups

Noor Alam, Noor Mohammad Khan


We show that a regular semigroups satisfying certain conditions in the containing semigroup is closed. As immediate corollaries, we have got that the special semigroup amalgam ~${\cal U} = [\{S,S'\};~U;~\{i,\alpha\mid U\}]$ within the class of left [right] quasi-normal orthodox semigroups, $\cal{R}$[$\cal{L}$]-unipotent semigroups and left[right] Clifford semigroups is embeddable in a left [right] quasi-normal orthodox semigroup, $\cal{R}$[$\cal{L}$]-unipotent semigroup and left[right] Clifford semigroup respectively. Finally we have shown that the class of all semigroups satisfying the identity $xyz=xz$ and the class of all semigroups satisfying the identity $xy=xyx[yx=xyx]$ are closed within the class of all semigroups satisfying the identities $xyz=xz$ and $xy=xyx[yx=xyx]$ repectively.

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Noor Alam, Noor Mohammad Khan, Epimorphisms, dominions and regular semigroups, J. Semigroup Theory Appl., 1 (2012), 34-45

Copyright © 2012 Noor Alam, Noor Mohammad Khan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Journal of Semigroup Theory and Applications

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