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On finiteness conditions for Rees matrix semigroups
Authors:Hayrullah Ayik
Institution:(1) Department of Mathematics, Cukurova University, 01330 Adana, Turkey
Abstract:Let T=phmmatS; 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.
Keywords:Rees matrix semigroup  periodicity  local finiteness  residual finiteness  word problem
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