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