On finiteness conditions for Rees matrix semigroups
Hayrullah Ayık · Czechoslovak Mathematical Journal · 2005
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.