Linear identities in graph algebras
We find the basis of all linear identities which are true in the variety of entropic graph algebras. We apply it to describe the lattice of all subvarieties of power entropic graph algebras.
Medial modes and rectangular algebras
Medial modes, a natural generalization of normal bands, were investigated by Płonka. Rectangular algebras, a generalization of rectangular bands (diagonal modes) were investigated by Pöschel and Reichel. In this paper we show that each medial mode embeds as a subreduct into a semimodule over a certain ring, and that a similar theorem holds for each Lallement sum of cancellative modes over a medial mode. Similar results are obtained for rectangular algebras. The paper generalizes earlier results...
Minimal compatible tolerances on lattices
Minimal generics from subvarieties of the clone extension of the variety of Boolean algebras
Let τ be a type of algebras without nullary fundamental operation symbols. We call an identity φ ≈ ψ of type τ clone compatible if φ and ψ are the same variable or the sets of fundamental operation symbols in φ and ψ are nonempty and identical. For a variety of type τ we denote by the variety of type τ defined by all clone compatible identities from Id(). We call the clone extension of . In this paper we describe algebras and minimal generics of all subvarieties of , where is the variety of...
Mittelwertstrukturen.
Modularity and distributivity of the lattice of -closed subsets of an algebraic structure
Let be an algebraic structure of type and a set of open formulas of the first order language . The set of all subsets of closed under forms the so called lattice of -closed subsets of . We prove various sufficient conditions under which the lattice is modular or distributive.
Monotonic valuations and valuations of triads of higher types
Nearly-idempotent plain algebras are indeed nearly idempotent plain algebras
Near-Rings of Polynomials over ...-Groups.
Note on homomorphisms of direct products of algebras
Notes on distributive groupoids
Notes on lattice congruences
Notes on left distributive groupoids
On a Generalization of Permutable Equivalence Relations
On a mechanism of defining morphisms in concrete categories
On a power of relational structures
On a Question of J. Hashimoto
On a representation of semigroups by products of algebras and relations
On a simple one-element extension of left zero semigroups
On algebraic operations of a lattice-ordered group