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15.743  Articles
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We introduce a notion of dimension of an algebraic lattice and, treating such a lattice as the congruence lattice of an algebra, we introduce the dimension of an algebra, too. We define a star-product as a special kind of subdirect product. We obtain the ... see more

We describe here a special subdirect decomposition of algebras with modular congruence lattice. Such a decomposition (called a star-decomposition) is based on the properties of the congruence lattices of algebras. We consider four properties of lattices: ... see more

The adjoint representations of several small dimensional Lie algebras  on their universal enveloping algebras  are explicitly decomposed. It is shown that commutants of raising operators are generated as polynomials in several basic elements. Th... see more

In today's team-based software development, good commit messages - comments on changes made in natural language - are essential. The metric for evaluating a commit message is its relevance. A good commit message should not only describe the changes made, ... see more


Traditional methods including algebra and category theory have some deficiencies in analyzing semantics properties and describing inductive rules of inductive data types, we present a method based on Fibrations theory aiming at those questions above. We s... see more

A basic tool in universal algebra is that of a congruence. It has been shown that congruences can be defined  for graphs with properties similar to their universal algebraic counterparts. In particular, a subdirect product of graphs and hence also a ... see more

It is known that commutative algebras satisfying the identity of degree four ((yx)x)x + ?((xx)x) = 0, with ? in the field and ? ? —1 are locally nilpotent. In this paper we study the birrepresentations of an algebra A that belongs to a... see more

The article deals with the method of signal restoration at the input of a nonlinear dynamic object with distributed parameters. To describe these objects, a universal mathematical model in the form of a Volterra integro-degree series has been chosen. The ... see more

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