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On finiteness conditions for Rees matrix semigroups

Hayrullah Ayik (2005)

Czechoslovak Mathematical Journal

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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