Semigroup varieties of inflations of unions of groups.
Semi-groupes à générations bornées
Semigroups satisfying xy = yg (x,y)x.
Semigroups with idempotent powers, I.
Semigroups with idempotent powers, II: The lattices of equational subclasses of [(xy2 =xy] .
Semilattice decomposition of n(2)-permutable semigroups.
Separative P.I. semigroups are embeddable into a semilattice of groups.
Sets of lengths do not characterize numerical monoids.
Sets with two associative operations
In this paper we consider duplexes, which are sets with two associative binary operations. Dimonoids in the sense of Loday are examples of duplexes. The set of all permutations carries a structure of a duplex. Our main result asserts that it is a free duplex with an explicitly described set of generators. The proof uses a construction of the free duplex with one generator by planary trees.
Solvability and the permutation property in inverse semigroups.
Solvable word problems in semigroups.
Solving word equations
Some commutativity criteria. - II
Some decidable congruences of free monoids
Let be the free monoid over a finite alphabet . We prove that a congruence of generated by a finite number of pairs , where and , is always decidable.
Some decision problems on integer matrices
Given a finite set of matrices with integer entries, consider the question of determining whether the semigroup they generated 1) is free; 2) contains the identity matrix; 3) contains the null matrix or 4) is a group. Even for matrices of dimension , questions 1) and 3) are undecidable. For dimension , they are still open as far as we know. Here we prove that problems 2) and 4) are decidable by proving more generally that it is recursively decidable whether or not a given non singular matrix belongs...
Some decision problems on integer matrices
Given a finite set of matrices with integer entries, consider the question of determining whether the semigroup they generated 1) is free; 2) contains the identity matrix; 3) contains the null matrix or 4) is a group. Even for matrices of dimension 3, questions 1) and 3) are undecidable. For dimension 2, they are still open as far as we know. Here we prove that problems 2) and 4) are decidable by proving more generally that it is recursively decidable whether or not a given non singular matrix belongs...
Some embedding theorems in varieties of semigroups.
Some Recent Results on Squarefree Words
Some remarks on possible generalized inverses in semigroups.
Some remarks on the four-spiral semigroup.