# Interassociates of a free semigroup on two generators

Author
Department of Mathematical Analysis and Algebra, Institute of Physics, Mathematics and Information Technologies, Luhansk Taras Shevchenko National University
Abstract
For any semigroup $(S;\cdot)$ let $(S;\circ)$ be a semigroup defined on the same set. Semigroup $(S;\circ)$ is called an interassociate of $(S;\cdot)$ if the following identities hold $x\cdot (y \circ z)=(x \cdot y) \circ z$ and $x \circ (y \cdot z)=(x \circ y) \cdot z$. All interassociates of the free semigroup over the two-element alphabet are described.
Keywords
free semigroup; interassociativity; interassociate of a semigroup
Reference
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Pages
139-145
Volume
41
Issue
2
Year
2014
Journal
Matematychni Studii
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