A method for enumerating cosets of a group presented by a canonical system
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
String-rewriting systems
A finiteness condition for rewriting systems
Theoretical Computer Science
Finite derivation type implies the homological finiteness condition FP3
Journal of Symbolic Computation
Finite derivation type for semi-direct products of monoids
Theoretical Computer Science
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This paper introduces the topological finiteness condition finite derivation type (FDT) on the class of semigroups. This notion is naturally extended from the monoid case. With this new concept we are able to prove that if a Rees matrix semigroup M[S; I, J; P] has FDT then the semigroup S also has FDT. Given a monoid S and a finitely presented Rees matrix semigroup M[S; I, J; P] we prove that if the ideal of S generated by the entries of P has FDT, then so does M[S; I, J; P]. In particular, we show that, for a finitely presented completely simple semigroup M, the Rees matrix semigroup M = M[S; I, J; P] has FDT if and only if the group S has FDT.