Note on homomorphisms of direct products of algebras
Notes on congruence implication
On a power of relational structures
On a variety of infinite algebras
On automorphisms of computability potential scales for -element algebras.
On free modes
We prove a theorem describing the equational theory of all modes of a fixed type. We use this result to show that a free mode with at least one basic operation of arity at least three, over a set of cardinality at least two, does not satisfy identities selected by ’A. Szendrei in Identities satisfied by convex linear forms, Algebra Universalis 12 (1981), 103–122, that hold in any subreduct of a semimodule over a commutative semiring. This gives a negative answer to the question raised by A. Romanowska:...
On mixed product of Boolean algebras
On reductive and distributive algebras
The paper investigates idempotent, reductive, and distributive groupoids, and more generally -algebras of any type including the structure of such groupoids as reducts. In particular, any such algebra can be built up from algebras with a left zero groupoid operation. It is also shown that any two varieties of left -step reductive -algebras, and of right -step reductive -algebras, are independent for any positive integers and . This gives a structural description of algebras in the join of...
On Semi-Boolean-Like Algebras
In a previous paper, we introduced the notion of Boolean-like algebra as a generalisation of Boolean algebras to an arbitrary similarity type. In a nutshell, a double-pointed algebra with constants is Boolean-like in case for all the congruences and are complementary factor congruences of . We also introduced the weaker notion of semi-Boolean-like algebra, showing that it retained some of the strong algebraic properties characterising Boolean algebras. In this paper, we continue the investigation...
On semisimple bands.
On some constructions of algebraic objects
Mono-unary algebras may be used to construct homomorphisms, subalgebras, and direct products of algebras of an arbitrary type.
On the failure of Birkhoff's theorem for locally small based equational categories of algebras
Positively prime models over a normal basic set.
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...
Remarks on Model Classes Acting on One Another.
Sheaf constructions in universal algebra and model theory
Simplicity of algebras requires to investigate almost all operations
Some decidable congruences of free monoids
Let be the free monoid over a finite alphabet . We prove that a congruence of generated by a finite number of pairs , where and , is always decidable.
Some decidable theories with finitely many covers which are decidable and algorithmically found
In any recursive algebraic language, I find an interval of the lattice of equational theories, every element of which has finitely many covers. With every finite set of equations of this language, an equational theory of this interval is associated, which is decidable with decidable covers that can be algorithmically found. If the language is finite, both this theory and its covers are finitely based. Also, for every finite language and for every natural number n, I construct a finitely based decidable...
Some embedding theorems.