In this paper, we assume that X is a BCK-algebra and y, t elements of X. We assign to these elements a set, denoted by F(y; t). We show that F(y; t) is a subalgebra of X. Then we prove that a BCK-algebra X is a Linear Commutative BCK-algebra if and only if every F(y; t) is an initial set of X. Moreover, we give a necessary and sufficient condition for F(y; t) to be an ideal. Finally, we show that the set consisting of all these sets forms a bounded distributive lattice.
Harizavi, H., & Koochakpoor, T. (2020). The smallest class of subalgebras of a commutative BCK-algebra containing initial subsets. Journal of Advanced Mathematical Modeling, 10(1), 158-171. doi: 10.22055/jamm.2020.28257.1678
MLA
Habib Harizavi; Tayebeh Koochakpoor. "The smallest class of subalgebras of a commutative BCK-algebra containing initial subsets". Journal of Advanced Mathematical Modeling, 10, 1, 2020, 158-171. doi: 10.22055/jamm.2020.28257.1678
HARVARD
Harizavi, H., Koochakpoor, T. (2020). 'The smallest class of subalgebras of a commutative BCK-algebra containing initial subsets', Journal of Advanced Mathematical Modeling, 10(1), pp. 158-171. doi: 10.22055/jamm.2020.28257.1678
VANCOUVER
Harizavi, H., Koochakpoor, T. The smallest class of subalgebras of a commutative BCK-algebra containing initial subsets. Journal of Advanced Mathematical Modeling, 2020; 10(1): 158-171. doi: 10.22055/jamm.2020.28257.1678
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