Formal Translation Monoid and Algebra Congruences in a Monodial Category.
Four notes on quasiorder lattices
Four-part semigroups - semigroups of Boolean operations
Four-part semigroups form a new class of semigroups which became important when sets of Boolean operations which are closed under the binary superposition operation f + g := f(g,...,g), were studied. In this paper we describe the lattice of all subsemigroups of an arbitrary four-part semigroup, determine regular and idempotent elements, regular and idempotent subsemigroups, homomorphic images, Green's relations, and prove a representation theorem for four-part semigroups.
Free algebras and automata realizations in the language of categories
Free algebras on a fixed set
Free groupoids with axioms of the form and/or .
Free Term Algebras
We interoduce a new characterization of algebras of normal forms of term rewriting systems [35] as algerbras of term free in itself (any function from free generators into the algebra generates endomorphism of the algebra). Introduced algebras are free in classes of algebras satisfying some sets of equalities. Their universes are subsets of all terms and the denotations of operation symbols are partially identical with the operations of construction of terms. These algebras are compiler algebras...
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...
From hereditary classes to varieties in abstract model theory and partial algebra
Function classes and relational constraints stable under compositions with clones
The general Galois theory for functions and relational constraints over arbitrary sets described in the authors' previous paper is refined by imposing algebraic conditions on relations.
Function minimum associated to a congruence on integral n-tuple space.
Functional Completeness and Automorphisms. II.
Functional Completeness and Automorphisms.I.
Functional completeness in pseudocomplemented de Morgan algebras
Functional representation of preiterative/combinatory formalism
Funktionen über lokal endlichen Halbordnungen.
Funktionen über lokal endlichen Halbordnungen II.
Further conclusions on functional completeness
Fuzzy congruences on groups and rings.
Fuzzy data in statistics
The development of effective methods of data processing belongs to important challenges of modern applied mathematics and theoretical information science. If the natural uncertainty of the data means their vagueness, then the theory of fuzzy quantities offers relatively strong tools for their treatment. These tools differ from the statistical methods and this difference is not only justifiable but also admissible. This relatively brief paper aims to summarize the main fuzzy approaches to vague data...