Abstract
Let T=ℳ[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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Ayik, H. On finiteness conditions for Rees matrix semigroups. Czech Math J 55, 455–463 (2005). https://doi.org/10.1007/s10587-005-0035-8
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DOI: https://doi.org/10.1007/s10587-005-0035-8