Finite basis theorem for systems of semigroup identities.
Finite binary relations have no more complexity than finite semigroups.
Finite communative semigroups having Frobenius semigroup algebras.
Finite commutative monoids of open maps
Finite globally idempotent semigroups.
Finite images and elementary equivalence of completely regular inverse semigroups.
Finite monoids having isotypical regular representations.
Finite semigroups admitting ring structure
Finitely generated free *-bands.
Finitely generated left commutative semigroups are residually finite.
Finitely generated left distributive semigoups
Finitely generated weakly reductive commutative semigroups.
Finiteness conditions for finitely generated monoids.
Finiteness conditions for semigroup rings
Finiteness of lattices of congruences on commutative semigroups.
Finiteness theorems for factorizations.
Finite-to-finite universal varieties of distributive double -algebras
Fixed point languages of rational transductions.
Fixed points of endomorphisms of certain free products
The fixed point submonoid of an endomorphism of a free product of a free monoid and cyclic groups is proved to be rational using automata-theoretic techniques. Maslakova’s result on the computability of the fixed point subgroup of a free group automorphism is generalized to endomorphisms of free products of a free monoid and a free group which are automorphisms of the maximal subgroup.
Fixed points of endomorphisms of certain free products
The fixed point submonoid of an endomorphism of a free product of a free monoid and cyclic groups is proved to be rational using automata-theoretic techniques. Maslakova’s result on the computability of the fixed point subgroup of a free group automorphism is generalized to endomorphisms of free products of a free monoid and a free group which are automorphisms of the maximal subgroup.