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http://dx.doi.org/10.4134/CKMS.2015.30.4.385

SEMI-PRIME CLOSURE OPERATIONS ON BCK-ALGEBRA  

BORDBAR, HASHEM (Faculty of Mathematics Statistics and Computer Science Shahid Bahonar University)
ZAHEDI, MOHAMMAD MEHDI (Department of Mathematics Graduate University of Advanced Technology)
Publication Information
Communications of the Korean Mathematical Society / v.30, no.4, 2015 , pp. 385-402 More about this Journal
Abstract
In this paper we study the (good) semi-prime closure operations on ideals of a BCK-algebra, lower BCK-semilattice, Noetherian BCK-algebra and meet quotient ideal and then we give several theorems that make different (good) semi-prime closure operations. Moreover by given some examples we show that the given different notions are independent together, for instance there is a semi-prime closure operation, which is not a good semi-prime. Finally by given the notion of "$c_f$-Max X", we prove that every member of "$c_f$-Max X" is a prime ideal. Also we conclude some more related results.
Keywords
BCI-algebra; BCK-algebra; closure operation; finite type closure operation; semi-prime closure operation;
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