Structure of ordered semirings.
This paper recalls some properties of a cyclic semigroup and examines cyclic subsemigroups in a finite ordered semigroup. We prove that a partially ordered cyclic semigroup has a spiral structure which leads to a separation of three classes of such semigroups. The cardinality of the order relation is also estimated. Some results concern semigroups with a lattice order.
The extension of a lattice ordered group by a generalized Boolean algebra will be denoted by . In this paper we apply subdirect decompositions of for dealing with a question proposed by Conrad and Darnel. Further, in the case when is linearly ordered we investigate (i) the completely subdirect decompositions of and those of , and (ii) the values of elements of and the radical .
In this note we characterize the one-generated subdirectly irreducible MV-algebras and use this characterization to prove that a quasivariety of MV-algebras has the relative congruence extension property if and only if it is a variety.
In this article, it will be shown that every -subgroup of a Specker -group has singular elements and that the class of -groups that are -subgroups of Specker -group form a torsion class. Methods of adjoining units and bases to Specker -groups are then studied with respect to the generalized Boolean algebra of singular elements, as is the strongly projectable hull of a Specker -group.
In this note we show that a subtraction algebra is equivalent to an implicative -algebra, and a subtraction semigroup is a special case of a -semigroup.
A subtraction semigroup is a semigroup with a further operation "" added, called subtraction and satisfying certain axioms. The paper concerns a problem by B. M. Schein concerning the structure of multiplication in a subtraction semigroup.