Related papers: Algebra with Conjugation
We investigate atomicity of free algebras and various forms of amalgamation for BL and MV algebras, and also Heyting algebras, though the latter algebras may not be linearly ordered, so strictly speaking their corresponding intuitionistic…
We prove an analogue of the Magnus theorem for associative algebras without unity over arbitrary fields. Namely, if an algebra is given by n+k generators and k relations and has an n-element system of generators, then this algebra is a free…
This note is to show the effectiveness of the notion of pseudoalgebra in the theory of conformal algebras. We adduce very simple construction of free associative conformal algebra and find its linear basis. There is no any new result but we…
We give an accessible introduction into the theory of lower central series of associative algebras, exhibiting the interplay between algebra, geometry and representation theory that is characteristic for this subject, and to discuss some…
In this survey I should like to introduce some concepts of algebraic geometry and try to demonstrate the fruitful interaction between algebraic geometry and computer algebra and, more generally, between mathematics and computer science. One…
Algebraic and combinatorial properties of a monomial ideal and its radical are compared.
This paper is the first in a series of three, the aim of which is to lay the foundations of algebraic geometry over the free metabelian Lie algebra $F$. In the current paper we introduce the notion of a metabelian Lie $U$-algebra and…
We define a new cohomology for associative algebras which we compute for algebras with units.
In this article we shows some results about algebra with the group of units having special polynomial identity.
We construct free cubic implication algebras with finitely many generators, and determine the size of these algebras.
In this note, we give a new characterization for an algebra to be $\qo$-compact in terms of {\em super-product operations} on the lattice of congruences of the relative free algebra.
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…
This paper characterizes the unital C*-algebra generated by a single invertible element as the unital free product of C[0,1] and C(T). To do this, I develop techniques to split and merge presentations of C*-algebras using free products in…
There are two established gradings on Leavitt path algebras associated with ultragraphs, namely the grading by the integers group and the grading by the free group on the edges. In this paper, we characterize properties of these gradings in…
We consider some natural generalizations to the class of all GLP-algebras of the so-called reduction property for reflection algebras in arithmetic. An analogue of this property is established for the free GLP-algebras and for some…
In this paper we construct free Hom-semigroups when its unary operation is multiplicative and is an involution. Our method of construction is by bracketed words. As a consequence, we obtain free Hom-associative algebras generated by a set…
We study the relation between algebraic structures and Graph Theory. We have defined five different weighted digraphs associated to a finite dimensional algebra over a field in order to tackle important properties of the associated…
The main aim of this paper to show how commutative algebra is connected to topology. We give underlying topological idea of some results on completable unimodular rows.
Recently, the author characterized all artinian square-free rings with identity. Here, those results are extended to the setting of rings with local units. We use this characterization of square-free rings to derive many results similar to…
We investigate commutator operations on compatible uniformities of an algebra. We present a commutator operation for compatible uniformities of an algebra in a congruence-modular variety which extends the commutator on congruences, and…