The aim of this paper is to classify all monogenic ternary semigroups, up to isomorphism. We divide them to two groups: finite and infinite. We show that every infinite monogenic ternary semigroup is isomorphic to the ternary semigroup O, the odd positive integers with ordinary addition. Then we prove that all finite monogenic ternary semigroups with the same index...

In this paper we investigate some properties of congruences on ternary semigroups. We also define the notion of congruence on a ternary semigroup generated by a relation and we determine the method of obtaining a congruence on a ternary semigroup T from a relation R on T. Furthermore we study the lattice of congruences on a ternary semigroup and we show that this lattice is not generally modular...

A ternary semigroup is a nonempty set together with a ternary multiplication which is associative. Any semigroup can be reduced to a ternary semigroup but a ternary semigroup does not necessarily reduce to a semigroup. The notion of fuzzy sets was introduced by Zadeh in 1965 and that of rough sets by Pawlak in 1982. Applications of the fuzzy set theory and rough set theory have been found in va...

It is shown that every finitely generated inverse subsemigroup (submonoid) of the monogenic free inverse semigroup (monoid) is finitely presented. As a consequence, the homomorphism and the isomorphism problems for the monogenic free inverse semigroup (monoid) are proved to be decidable.

T then it is proved that (1) ) ( ) ( ) ( 0 1 2 A N A N A N A    (2) N0(A) = A2, N1(A) is a semiprime ideal of T containing A, N2(A) = A4 are equivalent, where No(A) = The set of all A-potent elements in T, N1(A) = The largest ideal contained in No(A), N2(A) = The union of all A-potent ideals. If A is a semipseudo symmetric ideal of a ternary semigroup then it is proved that N0(A) = N1(A) = N...

We introduce the concept of bipolar (λ, δ)-fuzzification of a ternary semigroup and discuss some structural properties of bipolar (λ, δ)-fuzzy ideals of a ternary semigroup. Mathematics Subject Classification: 20N10, 20M12, 03E72

We define algebras of triple semigroup and DeMorgan triple semigroup and by defining three Mann’s compositions and one unary operation on the set of 3-place(ternary) functions over some set, we construct a DeMorgan triple semigroup of 3-place (ternary) functions and so find an abstract characterization of this algebras.

In this paper, we introduced the concepts of roughness and fuzziness in ordered ternary semigroups. We proved that the lower and upper approximation of an ordered ternary subsemigroup (resp. left ideal, right ideal, lateral ideal, bi-ideal, interior ideal) in an ordered ternary semigroup is an ordered ternary subsemigroup (resp. left ideal, right ideal, lateral ideal, bi-ideal, interior ideal)....