Sage Journals: Discover world-class research

Abstract

In this paper, the notions of commutators and pseudo commutators of elements (subsets) of a BCI-algebra are introduced and some properties are given. The concept of solvable BCI-algebras are also discussed and their properties are investigated. It is proved that the class of solvable BCI-algebras is closed under sub-algebra, cartesian product and inverse image operations.

Keywords

(pseudo) commutators derived sub-algebra

Get full access to this article

View all access options for this article.

References

Arai

, Iséki

and Tanaka

, Characterizations of BC, BC-algebra, Proc Japan Acad42 (1966), 105–107.

Arai

and Iséki

, On axiom systems of propositional calculi XIV, Proc Japan Academy42 (1966), 19–22.

Iséki

, On BCI-algebras, Math Sem Notes8 (1980), 125–130.

Iséki

and Tanaka

, An introduction to theory of BCK-algebras, Math Japon23 (1978), 1–26.

Iséki

, Some properties of BCK-algebras, Math Sem Notes2 (1974), 361–366.

Iséki

, An algebras related with a propositional calculus, Math Japon42 (1966), 26–29.

Meng

and Jun

Y.B.

, BCK-algebras, Kyung Moon Sa Co., Seoul, Korea, 1994.

Najafi

, Pseudo-Commutators in BCK-algebras, Pure Mathematical Sciences2 (2013), 29–32.

Najafi

and Borumand

, Saeid, Solvable BCK-algebras, Cankaya University Journal of Science and Engineering11 (2014), 19–28.

Commutators in BCI -algebras

Abstract

Keywords

Get full access to this article

References