-systems of unary algebras. I: On maximal and greatest -classes of the direct product of unary algebras
-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...
Random seminormed spaces
Range sets and partition sets in connection with congruences and algebraic invariants.
Rectangular groupoids
Recursive coalgebras of finitary functors
For finitary set functors preserving inverse images, recursive coalgebras A of Paul Taylor are proved to be precisely those for which the system described by A always halts in finitely many steps.
Recursive inseparability of the sets of identically valid and finitely refutable formulas of some elementary theories of varieties.
Reduced dimension of primitive classes of universal algebras
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.
Reflexive and antisymmetric relations and their systems
Reflexive relations and Mal'tsev conditions for congruence lattice identities in modular varieties
Reg-strongly solid varieties of commutative semigroups
Regular elements and Green's relations in Menger algebras of terms
Defining an (n+1)-ary superposition operation on the set of all n-ary terms of type τ, one obtains an algebra of type (n+1,0,...,0). The algebra n-clone τ is free in the variety of all Menger algebras ([9]). Using the operation there are different possibilities to define binary associative operations on the set and on the cartesian power . In this paper we study idempotent and regular elements as well as Green’s relations in semigroups of terms with these binary associative operations...
Regular elements of the semigroup of all binary relations.
Regular lattices
Regularising natural dualities.
Regularity and permutability via transferability of tolerances
Regularity and transitivity of local-automorphism semigroups of locally finite forests