If P is an upper semilattice whose Hasse diagram is a tree and whose cartesian powers are Macaulay, it is shown that Hasse diagram of P is actually a spider in which all the legs have the same length.

We prove that the semirings of 1-preserving and of 0,1preserving endomorphisms of a semilattice are always subdirectly irreducible and we investigate under which conditions they are simple. Subsemirings are also investigated in a similar way.

Let S be a multiplicatively idempotent congruence-simple semiring. We show that $$|S|=2$$ if has absorbing element. also prove is finite then either or $$S\cong {{\,\textrm{End}\,}}(L)$$ $$S^{op}\cong where L the 2-element semilattice. It seems to an open question, whether can infinite at all.

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...

I define the concepts of multifuncoid (and completary multifuncoid) and upgrading. Then I conjecture that upgrading of certain multifuncoids are multifuncoids (and that upgrading certain completary multifuncoids are completary multifuncoids). I have proved the conjectures for n 6 2. This short article is the first my public writing where I introduce the concept of multidimensional funcoid which...

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...