Here we study the principal left k-radicals of a semiring with semilattice additive reduct and characterize semirings which are disjoint union via −→ transitive closure l ∞ relation −→l on S, given by for a, b ∈ ⇔ bn Sa some n N.

Khutoretskii’s Theorem states that the Rogers semilattice of any family of c.e. sets has either at most one or infinitely many elements. A lemma in the inductive step of the proof shows that no Rogers semilattice can be partitioned into a principal ideal and a principal filter. We show that such a partitioning is possible for some family of d.c.e. sets. In fact, we construct a family of c.e. se...

By a Boolean inverse semigroup we mean an inverse semigroup whose semilattice of idempotents is a Boolean algebra. We study representations of a given inverse semigroup S in a Boolean inverse semigroup which are tight in a certain well defined technical sense. These representations are supposed to preserve as much as possible any trace of Booleannes present in the semilattice of idempotents of ...

A strong reducibility relation between partial numberings is introduced which is such that the reduction function transfers exactly the numbers which are indices under the numbering to be reduced into corresponding indices of the other numbering. The degrees of partial numberings of a given set with respect to this relation form an upper semilattice. In addition, Ershov’s completion constructio...

in this paper we define the notions of ultra and involution ideals in bck-algebras. then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. specially, we show that in a bounded implicative bck-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower bck-semilattice, the notions of...

The 0-distributive semilattice is characterized in terms of semiideals, ideals and filters. Some sufficient conditions and some necessary conditions for 0-distributivity are obtained. Counterexamples are given to prove that certain conditions are not necessary and certain conditions are not sufficient.

We study computably enumerable equivalence relations (ceers), under the reducibility R ≤ S if there exists a computable function f such that x R y if and only if f(x) S f(y), for every x, y. We show that the degrees of ceers under the equivalence relation generated by ≤ form a bounded poset that is neither a lower semilattice, nor an upper semilattice, and its first order theory is undecidable....

We study how the existence in an algebraic lattice L of a chain of a given type is reflected in the join-semilattice K(L) of its compact elements. We show that for every chain α of size κ, there is a set B of at most 2 join-semilattices, each one having a least element such that an algebraic lattice L contains no chain of order type I(α) if and only if the join-semilattice K(L) of its compact e...