On rich monoids
On semidirect and two-sided semidirect products of finite trivial monoids
On semigroups admitting ring structure.
On semigroups admitting ring structure III
On Semigroups Defined by the Identity xxy = y
On semigroups with least generating sets.
On some finiteness conditions in semigroup and group theory.
On some free semigroups, generated by matrices
Let We call a complex number “semigroup free“ if the semigroup generated by and is free and “free” if the group generated by and is free. First families of semigroup free ’s were described by J. L. Brenner, A. Charnow (1978). In this paper we enlarge the set of known semigroup free ’s. To do it, we use a new version of “Ping-Pong Lemma” for semigroups embeddable in groups. At the end we present most of the known results related to semigroup free and free numbers in a common picture....
On some non-rational congruences on free commutative semigroups.
On some presentations of completely regular semigroups.
On some subsemigroups of a free semigroup.
On subsemigroup lattices of aperiodic groups.
On subsemigroups of transformation semigroups with two generators.
On the arithmetic of arithmetical congruence monoids
Let ℕ represent the positive integers and ℕ₀ the non-negative integers. If b ∈ ℕ and Γ is a multiplicatively closed subset of , then the set is a multiplicative submonoid of ℕ known as a congruence monoid. An arithmetical congruence monoid (or ACM) is a congruence monoid where Γ = ā consists of a single element. If is an ACM, then we represent it with the notation M(a,b) = (a + bℕ₀) ∪ 1, where a, b ∈ ℕ and a² ≡ a (mod b). A classical 1954 result of James and Niven implies that the only ACM...
On the Burnside problem for semigroups of matrices in the (max, + ) algebra.
On the complexity of the word problem for finitely presented commutative semigroups.
On the construction of bisimple orthodox semigroups.
On the decidability of semigroup freeness∗
This paper deals with the decidability of semigroup freeness. More precisely, the freeness problem over a semigroup S is defined as: given a finite subset X ⊆ S, decide whether each element of S has at most one factorization over X. To date, the decidabilities of the following two freeness problems have been closely examined. In 1953, Sardinas and Patterson proposed a now famous algorithm for the freeness problem over the free monoids....
On the decidability of semigroup freeness
This paper deals with the decidability of semigroup freeness. More precisely, the freeness problem over a semigroup S is defined as: given a finite subset X ⊆ S, decide whether each element of S has at most one factorization over X. To date, the decidabilities of the following two freeness problems have been closely examined. In 1953, Sardinas and Patterson proposed a now famous algorithm for the freeness problem over the free monoids. In 1991, Klarner, Birget and Satterfield proved the undecidability...
On the decidability of semigroup freeness∗
This paper deals with the decidability of semigroup freeness. More precisely, the freeness problem over a semigroup S is defined as: given a finite subset X ⊆ S, decide whether each element of S has at most one factorization over X. To date, the decidabilities of the following two freeness problems have been closely examined. In 1953, Sardinas and Patterson proposed a now famous algorithm for the freeness problem over the free monoids....