Abstract:
In this paper , we define a new type of ideal on a non associative seminear-ring with BCK algebra (NASNR-BCK algebra) which is called SM- ideal where we say that (X , . , * , 0) is a NASNR-BCK algebra if X is a non-empty set with two binary operations '*' and '.' defined on it and 0 is constant satisfying the following conditions :
a) (X , . ) is a semigroup .
b) (X, *, 0) is a BCK algebra.
c) (x . y) * z = (x *z) . (y * z) , for all x, y, z X which is called thedistributive law
d) 0 . x = x . 0 = x , for all x X.
We prove some results then we define the notion of fuzzy SM-ideal on NASNR-BCK algebra and prove some results with examples.We explain the relationships among it and other type of ideals on NASNR-BCK algebra.
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