On finiteness conditions for Rees matrix semigroups |
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Authors: | Hayrullah Ayik |
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Institution: | (1) Department of Mathematics, Cukurova University, 01330 Adana, Turkey |
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Abstract: | Let T= S; I; J; P] be a Rees matrix semigroup where S is a semigroup, I and J are index sets, and P is a J × I matrix with entries from S, and let U be the ideal generated by all the entries of P. If U has finite index in S, then we prove that T is periodic (locally finite) if and only if S is periodic (locally finite). Moreover, residual finiteness and having solvable word problem are investigated. |
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Keywords: | Rees matrix semigroup periodicity local finiteness residual finiteness word problem |
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