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...
Endomorphism kernel property for finite groups
A group has the endomorphism kernel property (EKP) if every congruence relation on is the kernel of an endomorphism on . In this note we show that all finite abelian groups have EKP and we show infinite series of finite non-abelian groups which have EKP.
Endomorphisms and connected components of partial monounary algebras
Endomorphisms of partial monounary algebras
Epimorphisms between finite MV-algebras
MV-algebras were introduced by Chang to prove the completeness of the infinite-valued Łukasiewicz propositional calculus. Recently, algebraic theory of MV-algebras has been intensively studied. Wajsberg algebras are just a reformulation of Chang MV-algebras where implication is used instead of disjunction. Using these equivalence, in this paper we provide conditions for the existence of an epimorphism between two finite MV-algebras and . Specifically, we define the mv-functions with domain in...
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...
Equimorphy in varieties of double Heyting algebras
We show that any finitely generated variety V of double Heyting algebras is finitely determined, meaning that for some finite cardinal n(V), any class ⊆ V consisting of algebras with pairwise isomorphic endomorphism monoids has fewer than n(V) pairwise non-isomorphic members. This result complements the earlier established fact of categorical universality of the variety of all double Heyting algebras, and contrasts with categorical results concerning finitely generated varieties of distributive...
Equivalence relations defined by automorphism groups
Equivalence Systems with Finitely Many Relations.
Existence of monomorphisms of partial unary algebras