FREE BOUNDED COMMUTATIVE BCK-ALGEBRA WITH ONE FREE GENERATOR

Free Extended BCK-Module

In this paper, by considering the notion of extended BCK-module, we define the concepts of free extended BCK-module, free object in category of extended BCK-modules and we state and prove some related results. Specially, we define the notion of idempotent extended BCK-module and we get some important results in free extended BCK-modules. In particular, in category of idempotent extended BCK-mod...

On Commutative Algebra and Characteristic-free Representation Theory

A description of the thread holding together commutative algebra, homological algebra and representation theory. A discussion of some of the developments in the area of determinantal ideals, Schur and Weyl modules, and their interrelationships.

Anti-commutative Gröbner-Shirshov basis of a free Lie algebra

One of the natural ways to prove that the Hall words (Philip Hall, 1933) consist of a basis of a free Lie algebra is a direct construction: to start with a linear space spanned by Hall words, to define the Lie product of Hall words, and then to check that the product yields the Lie identities (Marshall Hall, 1950). Here we suggest another way using the Composition-Diamond lemma for free anti-co...

Commutative Algebra Commutative Algebra : General

Dual Bck - Algebra and Mv - Algebra

The aim of this paper is to study the properties of dual BCK-algebra and to prove that the MV -algebra is equvalent to the bounded commutative dual BCK-algebra.