A non-commutative free algebra of rank 0
A normal form for restricted exponential functions
A note on cylindric lattices
0. Introduction. Besides being of intrinsic interest, cylindric (semi-) lattices arise naturally from the study of dependencies in relational databases; the polynomials on a cylindric semilattice are closely related to the queries obtainable from project-join mappings on a relational database (cf. [D] for references). This note is intended to initiate the study of these structures, and only a few, rather basic results will be given. Some problems at the end will hopefully stimulate further research....
A note on dual discriminator varieties.
A note on finite sets of terms closed under subterms and unification
The paper contains two remarks on finite sets of groupoid terms closed under subterms and the application of unifying pairs.
A note on idempotent modifications of groups
The idempotent modification of a group is always a subdirectly irreducible algebra.
A note on normal varieties of monounary algebras
A variety is called normal if no laws of the form are valid in it where is a variable and is not a variable. Let denote the lattice of all varieties of monounary algebras and let be a non-trivial non-normal element of . Then is of the form with some . It is shown that the smallest normal variety containing is contained in for every where denotes the operator of forming choice algebras. Moreover, it is proved that the sublattice of consisting of all normal elements of...
A note on permutability in varieties
A note on some varieties of point algebras
A note on square extensions of bands.
A note on the finite extensivity property
A note on varieties of unary algebras
A note on varieties with distributive subalgebra lattices
A property of the solvable radical in finitely decidable varieties
It is shown that in a finitely decidable equational class, the solvable radical of any finite subdirectly irreducible member is comparable to all congruences of the irreducible if the type of the monolith is 2. In the type 1 case we establish that the centralizer of the monolith is strongly solvable.
A reduction theorem for ring varieties whose subvariety lattice is distributive
We prove a theorem (for arbitrary ring varieties and, in a stronger form, for varieties of associative rings) which basically reduces the problem of a description of varieties with distributive subvariety lattice to the case of algebras over a finite prime field.
A remark on the ideal extension property
A scheme for congruence semidistributivity
A diagrammatic statement is developed for the generalized semidistributive law in case of single algebras assuming that their congruences are permutable. Without permutable congruences, a diagrammatic statement is developed for the ∧-semidistributive law.
A semantic construction of two-ary integers
To binary trees, two-ary integers are what usual integers are to natural numbers, seen as unary trees. We can represent two-ary integers as binary trees too, yet with leaves labelled by binary words and with a structural restriction. In a sense, they are simpler than the binary trees, they relativize. Hence, contrary to the extensions known from Arithmetic and Algebra, this integer extension does not make the starting objects more complex. We use a semantic construction to get this extension. This...
A semigroup in function algebra.
A simple basis of ideal terms of Brouwerian semilattices