Title of article :
Γ- BCK algebras
Author/Authors :
Borumand Saeid, Arsham Department of pure Mathematics - Facultu of Mathematics and Computer - Shahid Bahonar University of Kerman - Kerman, Iran , Krishna Rao, M Murali Department of Mathematics - Sankethika Institute of Tech. and Management - Visakhapatnam, India , Kona, R Kumar Department of Mathematics - GIS, GITAM (Deemed to be University) - Visakhapatnam, India
Abstract :
We know that Γ- ring, Γ- incline, Γ- semiring, Γ- semigroup are generalizations of ring, incline, semiring and semigroup respectively. In this paper, we introduce the concept of Γ- BCK-algebras as a general- ization of BCK-algebras and study Γ- BCK-algebras. We also introduce subalgebra, ideal, closed ideal, normal subalgebra, normal ideal and con- struct quotient of Γ- BCK-algebras. We prove that if f : M ! L be a normal homomorphism of Γ- BCK-algebras M and N; then Γ- BCK- algebra M=N is isomorphic to Im(f), where N = ker(f):
Keywords :
(Γ-)BCK-algebra , Quotient Γ- BCK-algebra , Subalgebra , Ideal , (Closed, Normal) Ideal
Journal title :
Journal of Mahani Mathematical Research Center
