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Zbl 0848.06016
Abujabal, H.A.S.; Aslam, M.; Thaheem, A.B.
On actions of BCK-algebras on groups. (English)
[J] Panam. Math. J. 4, No.3, 43-48 (1994). ISSN 1064-9735

We introduce a concept analogous to module theory. Given a BCK-algebra $X$, we define an $X$-module and provide a few examples. We also define related concepts like homomorphisms, kernels etc., and prove isomorphism theorems. Finally, we show that an algebra $(X, \wedge, \vee,*,1)$ modulo a congruence relation can be embedded in a semigroup of endomorphisms of an $X$-module.

MSC 2000:: *06F35 BCK-algebras, etc.

Keywords: module; BCK-algebra; homomorphisms; kernels; congruence; endomorphisms

Cited in: Zbl 1113.06022

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