UNARY FA-PRESENTABLE SEMIGROUPS

Unary FA-Presentable Semigroups

Automatic presentations, also called FA-presentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of interesting decision problems. A particular focus of research has been the classification of those structures of some species that admit automatic presentations. Whilst some successes have been obtained, this appears to be a difficult pro...

Subalgebras of FA-presentable algebras

Automatic presentations, also called FA-presentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of fundamental decision problems. This paper studies FA-presentable algebras. First, an example is given to show that the class of finitely generated FA-presentable algebras is not closed under forming finitely generated subalgebras, even wi...

FA-presentable Groups and Rings

We consider structures which are FA-presentable. It is known that an FA-presentable finitely generated group is virtually abelian; we strengthen this result by showing that an arbitrary FA-presentable group is locally virtually abelian. As a consequence, we prove that any FA-presentable ring is locally finite; this is a significant restriction and allows us to say a great deal about the structu...

On varieties of semigroups and unary algebras∗†

The elementary result of Variety theory is Eilenberg’s Variety theorem which was motivated by characterizations of several families of string languages by syntactic monoids or semigroups, such as Schützenberger’s theorem connecting star-free languages and aperiodic monoids. Eilenberg’s theorem has been extended in various directions. For example, Thérien involved varieties of congruences on fre...

Unary Semigroups with an Associate Subgroup