Free groupoids with axioms of the form and/or .
Free trees and the optimal bound in Wehrung's theorem
We prove that there is a distributive (∨,0,1)-semilattice of size ℵ₂ such that there is no weakly distributive (∨,0)-homomorphism from to with 1 in its range, for any algebra A with either a congruence-compatible structure of a (∨,1)-semi-lattice or a congruence-compatible structure of a lattice. In particular, is not isomorphic to the (∨,0)-semilattice of compact congruences of any lattice. This improves Wehrung’s solution of Dilworth’s Congruence Lattice Problem, by giving the best cardinality...
Function minimum associated to a congruence on integral n-tuple space.
Fuzzy congruences on groups and rings.
General algebraic geometry and formal concept analysis.
Generalized deductive systems in subregular varieties
An algebra is subregular alias regular with respect to a unary term function if for each we have whenever for each . We borrow the concept of a deductive system from logic to modify it for subregular algebras. Using it we show that a subset is a class of some congruence on containing if and only if is this generalized deductive system. This method is efficient (needs a finite number of steps).
Generalized ordering and partitions
Graphical Compositions and Weak Congruences
Green's relations and their generalizations on semigroups
Green's relations and their generalizations on semigroups are useful in studying regular semigroups and their generalizations. In this paper, we first give a brief survey of this topic. We then give some examples to illustrate some special properties of generalized Green's relations which are related to completely regular semigroups and abundant semigroups.
Group congruences on eventually inverse semigroups
Group congruences on regular semigroups.
Homegeneous groupoids
Homomorphic images of subdirectly irreducible groupoids
A groupoid is a homomorphic image of a subdirectly irreducible groupoid (over its monolith) if and only if has a smallest ideal.
Ideal extensions of graph algebras
Let and be graph algebras. In this paper we present the notion of an ideal in a graph algebra and prove that an ideal extension of by always exists. We describe (up to isomorphism) all such extensions.
Ideal nil-extensions of semigroups with semimodular congruence lattices.
Ideals and congruence kernels of algebras
Idempotent separating congruences on an orthodox semigroup via the least inverse congruence.
Implication algebras
We introduce the concepts of pre-implication algebra and implication algebra based on orthosemilattices which generalize the concepts of implication algebra, orthoimplication algebra defined by J.C. Abbott [2] and orthomodular implication algebra introduced by the author with his collaborators. For our algebras we get new axiom systems compatible with that of an implication algebra. This unified approach enables us to compare the mentioned algebras and apply a unified treatment of congruence properties....
Induced algebras
Interpolation in congruence permutable algebras