Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2015.06.05
  • Published : 2015.10.31

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.

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