E-INVERSIVE *-SEMIGROUPS
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초록
$(S,\ast)$ 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.
Abstract
$(S,\ast)$ 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.
참고문헌 (10)
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