Polynomial functions over monoids.
Polynomially determined congruences in algebras without constants
Polynomially determined tolerances
Prime Ideal Theorems and systems of finite character
We study several choice principles for systems of finite character and prove their equivalence to the Prime Ideal Theorem in ZF set theory without Axiom of Choice, among them the Intersection Lemma (stating that if is a system of finite character then so is the system of all collections of finite subsets of meeting a common member of ), the Finite Cutset Lemma (a finitary version of the Teichm“uller-Tukey Lemma), and various compactness theorems. Several implications between these statements...
Principal tolerances on lattices
Principal tolerances on lattices
Products of mode varieties and algebras of subalgebras
Propriétés de permanence et existence de réalisations minimales pour les algèbres multisortes
-systems of unary algebras. II: Maximal and minimal subalgebras of the direct products of unary algebras
Radical decompositions of semiheaps
Semiheaps are ternary generalisations of involuted semigroups. The first kind of semiheaps studied were heaps, which correspond closely to groups. We apply the radical theory of varieties of idempotent algebras to varieties of idempotent semiheaps. The class of heaps is shown to be a radical class, as are two larger classes having no involuted semigroup counterparts. Radical decompositions of various classes of idempotent semiheaps are given. The results are applied to involuted I-semigroups, leading...
Range sets and partition sets in connection with congruences and algebraic invariants.
Rees ideal algebras
We describe algebras and varieties for which every ideal is a kernel of a one-block congruence.
Refinement Monoids, Vaught Monoids, and Boolean Algebras.
Regular lattices
Regularity and permutability via transferability of tolerances
Regularity in p-algebras and p-semilattices
Regularity of algebras with applications to congruence class geometry
Relation products of congruences and factor congruences
Relational characterizations of permutable and -permutable varieties
Relational classes and their characterizations