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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.

On graph products of automatic monoids

A. Veloso Da Costa (2001)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

The graph product is an operator mixing direct and free products. It is already known that free products and direct products of automatic monoids are automatic. The main aim of this paper is to prove that graph products of automatic monoids of finite geometric type are still automatic. A similar result for prefix-automatic monoids is established.

On graph products of automatic monoids

A. Veloso da Costa (2010)

RAIRO - Theoretical Informatics and Applications

The graph product is an operator mixing direct and free products. It is already known that free products and direct products of automatic monoids are automatic. The main aim of this paper is to prove that graph products of automatic monoids of finite geometric type are still automatic. A similar result for prefix-automatic monoids is established.

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