The cardinal and the idempotent number of various monoids of transformations on a finite chain.
The cardinalities of the Green classes of the free objects in varieties of bands.
The ...-category of a monoid.
The category of totally symmetric quasigroups is binding
The catenary degree of Krull monoids I
Let be a Krull monoid with finite class group such that every class contains a prime divisor (for example, a ring of integers in an algebraic number field or a holomorphy ring in an algebraic function field). The catenary degree of is the smallest integer with the following property: for each and each two factorizations of , there exist factorizations of such that, for each , arises from by replacing at most atoms from by at most new atoms. Under a very mild condition...
The catgorical theory of self-similarity.
The center of translational hull and the hull of center of semigroup
The characterisation of monoids by properties of their S-systems.
The cofinality of a band.
The common right multiple property in semigroup rings.
The commutativity relation in the symmetric semigroup.
The compression semigroup of a cone is connected.
The concept of structural regularity.
The congruence class of an idempotent in a regular semigroup.
The congruence extension property for algebraic semigroups.
The congruences on S(X) which commute with V.
The connection between a (3,2)-semigroup automaton and a semigroup automaton
The construction of semigroups from groups and semilattices
The core congruence on a monoid.
The dimension of a variety
Derived varieties were invented by P. Cohn in [4]. Derived varieties of a given type were invented by the authors in [10]. In the paper we deal with the derived variety of a given variety, by a fixed hypersubstitution σ. We introduce the notion of the dimension of a variety as the cardinality κ of the set of all proper derived varieties of V included in V. We examine dimensions of some varieties in the lattice of all varieties of a given type τ. Dimensions of varieties of lattices and all subvarieties...