EDZ-varieties: The Schreier property and epimorphisms onto
Elementary equivalence for the lattices of subalgebras and automorphism groups of free algebras.
Embedding properties of endomorphism semigroups
Denote by PSelf Ω (resp., Self Ω) the partial (resp., full) transformation monoid over a set Ω, and by Sub V (resp., End V) the collection of all subspaces (resp., endomorphisms) of a vector space V. We prove various results that imply the following: (1) If card Ω ≥ 2, then Self Ω has a semigroup embedding into the dual of Self Γ iff . In particular, if Ω has at least two elements, then there exists no semigroup embedding from Self Ω into the dual of PSelf Ω. (2) If V is infinite-dimensional, then...
E-minimal semigroups.
Epimorphisms in some groupoid varieties
Equational Bases for Lattice Theories.
Equational bases for weak monounary varieties
It is well-known that every monounary variety of total algebras has one-element equational basis (see [5]). In my paper I prove that every monounary weak variety has at most 3-element equational basis. I give an example of monounary weak variety having 3-element equational basis, which has no 2-element equational basis.
Equational compactness in infinitary algebras
Equational Reformulation Of Formal Theories
Equational spectrum of Hilbert varieties
We prove that an equational class of Hilbert algebras cannot be defined by a single equation. In particular Hilbert algebras and implication algebras are not one-based. Also, we use a seminal theorem of Alfred Tarski in equational logic to characterize the set of cardinalities of all finite irredundant bases of the varieties of Hilbert algebras, implication algebras and commutative BCK algebras: all these varieties can be defined by independent bases of n elements, for each n > 1.
Equational theories of some almost unary groupoids
Equational Theories of Varieties defined by P-compatible Identities of Boole'an Algebras
Equimorphy in varieties of distributive double -algebras
Any finitely generated regular variety of distributive double -algebras is finitely determined, meaning that for some finite cardinal , any subclass of algebras with isomorphic endomorphism monoids has fewer than pairwise non-isomorphic members. This result follows from our structural characterization of those finitely generated almost regular varieties which are finitely determined. We conjecture that any finitely generated, finitely determined variety of distributive double -algebras...
E-varieties of regular semigroups, relatively bifree objects and fully invariant congruences.
Even equations and Agassiz sums
Every at most four element algebra has a Mal'cev theory for permutability
Extension theories for monoids.
Extension-closure and attainability for varieties of algebras with involution
Extensive varieties