Semidirectly closed pseudovarieties of locally trivial semigroups.
Semigroup varieties of inflations of unions of groups.
Semigroups and their lattice of congruences II.
Semigroups of order preserving mappings on a finite chain: a new class of divisors.
Semirings embedded in a completely regular semiring
Recently, we have shown that a semiring is completely regular if and only if is a union of skew-rings. In this paper we show that a semiring satisfying can be embedded in a completely regular semiring if and only if is additive separative.
Small idempotent clones. I
G. Grätzer and A. Kisielewicz devoted one section of their survey paper concerning -sequences and free spectra of algebras to the topic “Small idempotent clones” (see Section 6 of [18]). Many authors, e.g., [8], [14, 15], [22], [25] and [29, 30] were interested in -sequences of idempotent algebras with small rates of growth. In this paper we continue this topic and characterize all idempotent groupoids with (see Section 7). Such groupoids appear in many papers see, e.g. [1], [4], [21], [26,...
Solid varieties of semigroups.
Some (2, n) combinatorial Stein groupoids.
Some (2, n) combinatorial Stein groupoids. (Short Communication).
Some embedding theorems in varieties of semigroups.
Some pseudovariety joins involving the pseudovariety of finite groups.
Some quasi-ordered classes of finite commutative semigroups.
Some relations on the lattice of varieties of completely regular semigroups
On the lattice of varieties of completely regular semigroups considered as algebras with the binary multiplication and unary inversion within maximal subgroups, we study the relations , , , , , , and . Here is the kernel relation, is the trace relation, and are the left and the right trace relations, respectively, for , is the core relation and is the local relation. We give an alternative definition for each of these relations of the form for some subclasses of ....
Some results on C-varieties
In an earlier paper, the second author generalized Eilenberg's variety theory by establishing a basic correspondence between certain classes of monoid morphisms and families of regular languages. We extend this theory in several directions. First, we prove a version of Reiterman's theorem concerning the definition of varieties by identities, and illustrate this result by describing the identities associated with languages of the form (a1a2...ak)+, where a1,...,ak are distinct letters. Next,...
Some results on the dot-depth hierarchy.
Some results on -varieties
In an earlier paper, the second author generalized Eilenberg’s variety theory by establishing a basic correspondence between certain classes of monoid morphisms and families of regular languages. We extend this theory in several directions. First, we prove a version of Reiterman’s theorem concerning the definition of varieties by identities, and illustrate this result by describing the identities associated with languages of the form , where are distinct letters. Next, we generalize the notions...
Splitting left distributive semigroups
Strict radicals of monoids.
Sturdy frames of type (2,2) algebras and their applications to semirings
We introduce sturdy frames of type (2,2) algebras, which are a common generalization of sturdy semilattices of semigroups and of distributive lattices of rings in the theory of semirings. By using sturdy frames, we are able to characterize some semirings. In particular, some results on semirings recently obtained by Bandelt, Petrich and Ghosh can be extended and generalized.
Subalgebra lattices of completely simple semigroups.