Congruence Topologies on Universal Algebras.
Congruences and homomorphisms on -algebras
The topic of the paper are -algebras, where is a complete lattice. In this research we deal with congruences and homomorphisms. An -algebra is a classical algebra which is not assumed to satisfy particular identities and it is equipped with an -valued equality instead of the ordinary one. Identities are satisfied as lattice theoretic formulas. We introduce -valued congruences, corresponding quotient -algebras and -homomorphisms and we investigate connections among these notions. We prove...
Congruences and ideals in lattice effect algebras as basic algebras
Effect basic algebras (which correspond to lattice ordered effect algebras) are studied. Their ideals are characterized (in the language of basic algebras) and one-to-one correspondence between ideals and congruences is shown. Conditions under which the quotients are OMLs or MV-algebras are found.
Congruences and ideals in ternary rings
A ternary ring is an algebraic structure of type satisfying the identities and where, moreover, for any , , there exists a unique with . A congruence on is called normal if is a ternary ring again. We describe basic properties of the lattice of all normal congruences on and establish connections between ideals (introduced earlier by the third author) and congruence kernels.
Congruences and ideals on left divisible involutory groupoids
In [1] ideals and congruences on semiloops were investigated. The aim of this paper is to generalize results obtained for semiloops to the case of left divisible involutory groupoids.
Congruences associated with inverse transversals.
Congruences generated by filters
Congruences In Regular Categories.
Congruences of pseudocomplemented algebras
Congruences on an inverse Bruck-Reilly monoid. Part I: Non-group congruences.
Congruences on bands of π-groups
A semigroup S is said to be completely π-regular if for any a ∈ S there exists a positive integer n such that aⁿ is completely regular. The present paper is devoted to the study of completely regular semigroup congruences on bands of π-groups.
Congruences on Bruck-Reilly extensions of monoids.
Congruences on products in varieties satisfying the CEP
Congruences on semilattices with section antitone involutions
We deal with congruences on semilattices with section antitone involution which rise e.g., as implication reducts of Boolean algebras, MV-algebras or basic algebras and which are included among implication algebras, orthoimplication algebras etc. We characterize congruences by their kernels which coincide with semilattice filters satisfying certain natural conditions. We prove that these algebras are congruence distributive and 3-permutable.
Congruences on the subclones of the rank 3 Burle clone containing no creative functions.
Conjugated algebras
We generalize the correspondence between basic algebras and lattices with section antitone involutions to a more general case where no lattice properties are assumed. These algebras are called conjugated if this correspondence is one-to-one. We get conditions for the conjugary of such algebras and introduce the induced relation. Necessary and sufficient conditions are given to indicated when the induced relation is a quasiorder which has “nice properties", e.g. the unary operations are antitone...
Connected Algebras and Universal Covering
Construction of all homomorphisms of groupoids
Construction of all homomorphisms of mono--ary algebras
Construction of all strong homomorphisms of binary structures