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$(S,\ast)$ is a semigroup $S$ equipped with a unary operation $``\ast"$. This work is devoted to a class of unary semigroups, namely {\em $E$-inversive $\ast$-semigroups}. A unary semigroup $(S,\ast)$ is called an $E$-inversive $\ast$-semigroup if the following identities hold: \begin{center}$x^\ast x x^\ast=x^\ast, {(x^\ast)}^\ast=x x^\ast x, (xy)^\ast=y^\ast x^\ast$. \end{center} In this paper, $E$-inversive $\ast$-semigroups are characterized by several methods. Furthermore, congruences on these semigroups are also studied.
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참고문헌 (10)
참고문헌 신청
B. Weipoltshammer / 2002 / Certain congruences on E-inversive E-semigroups / Semigroup Forum 65 (2) : 233 ~ 248
J. M. Howie / 1976 / An Introduction to Semigroup Theory / Academic Press
M. Petrich / 1984 / Inverse Semigroups / John Wiley & Sons, Inc
M. Petrich / 1999 / Completely Regualr Semigroups / A Wiley-Interscience Publication
M. Yamada / 1982 / P-systems in regular semigroups / Semigroup Forum 24 (2-3) : 173 ~ 178
J. M. Howie / 1976 / An Introduction to Semigroup Theory / Academic Press
M. Petrich / 1984 / Inverse Semigroups / John Wiley & Sons, Inc
M. Petrich / 1999 / Completely Regualr Semigroups / A Wiley-Interscience Publication
M. Yamada / 1982 / P-systems in regular semigroups / Semigroup Forum 24 (2-3) : 173 ~ 178
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