Left and Right Magnifying Elements in the Semigroup of all Binary Relations

Watchara Teparos, Soontorn Boonta, Thitiya Theparod

Abstract

An element a of a semigroup S is called left [right] magnifying if there exists a proper subset M of S such that S = aM [S = M a]. Let X be a nonempty set and BX the semigroup of binary relations on X. In this paper, we give necessary and sufficient conditions for elements in BX to be left or right magnifying.

Keywords

Relations, functions, magnifying elements, the semigroup of all binary relations

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