• Title/Summary/Keyword: Semi neutral BCK-algebra

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SOLUTION OF AN UNSOLVED PROBLEM IN BCK-ALGEBRA

  • Nisar, Farhat;Bhatti, Shaban Ali
    • East Asian mathematical journal
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    • v.21 no.1
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    • pp.49-60
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    • 2005
  • In this paper we introduced Semi-neutral BCK-algebra and investigate some of its properties. The notions of ideals and subalgebras coincide in Semi-neutral BCK-algebras. We also show that if the number of nonzero elements in a Semi-neutral BCK-algebra is n, then the number of ideals/subalgebras in it is $2^n$. Further, we solved an open problem posed by W.A. Dudek in [2].

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SEMI-NEUTRAL GROUPOIDS AND BCK-ALGEBRAS

  • Kim, Hee Sik;Neggers, Joseph;Seo, Young Joo
    • Communications of the Korean Mathematical Society
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    • v.37 no.3
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    • pp.649-658
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    • 2022
  • In this paper, we introduce the notion of a left-almost-zero groupoid, and we generalize two axioms which play important roles in the theory of BCK-algebra using the notion of a projection. Moreover, we investigate a Smarandache disjointness of semi-leftoids.