Interassociates of a free semigroup on two generators

Author
A. B. Gorbatkov
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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