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Magnifying elements in a semigroup of transformations preserving equivalence relation

Ronnason Chinram|Thananya Kaewnoi|Montakarn Petapirak
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2019.06|한국수학논문집 (Korean Journal of Mathematics)|제27권 제2호|pp. 269-277

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키워드

magnifying elementstransformation semigroupsequivalence relations.
주제분류수학

초록

Let $X$ be a nonempty set, $\rho$ be an equivalence on $X$, $T(X)$ be the semigroup of all transformations from $X$ into itself, and $T_{\rho}(X) = \{f \in T(X) \mid (x,y) \in \rho$ implies $((x)f, (y)f) \in \rho\}$. In this paper, we investigate some necessary and sufficient conditions for elements in $T_{\rho}(X)$ to be left or right magnifying.

Abstract

Let $X$ be a nonempty set, $\rho$ be an equivalence on $X$, $T(X)$ be the semigroup of all transformations from $X$ into itself, and $T_{\rho}(X) = \{f \in T(X) \mid (x,y) \in \rho$ implies $((x)f, (y)f) \in \rho\}$. In this paper, we investigate some necessary and sufficient conditions for elements in $T_{\rho}(X)$ to be left or right magnifying.

참고문헌 (14)

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관련 논문AI추천

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