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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 ``$c_f\text{-Max}~X$", we prove that every member of ``$c_f\text{-Max}~X$" is a prime ideal. Also we conclude some more related results.
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참고문헌 (12)
참고문헌 신청
D. Kirby / 1969 / Closure Operations on Ideals and Submodules / J. London Math. Soc 44 : 283 ~ 291
E. H. Moore / 1910 / Introduction to a Form of General Analysis / The New Haven Mathematical Colloquium : 1 ~ 150
G. Birkhoff / 1967 / Lattice Theory / American Mathematical Society Colloquium Pub-lications
H. Bordbar / / (A finite type) Closure operations on BCK-algebra
H. Bordbar / 2014 / Some properties of closure operation on (Noetherian) BCK-algebra / 12th AHA congress
E. H. Moore / 1910 / Introduction to a Form of General Analysis / The New Haven Mathematical Colloquium : 1 ~ 150
G. Birkhoff / 1967 / Lattice Theory / American Mathematical Society Colloquium Pub-lications
H. Bordbar / / (A finite type) Closure operations on BCK-algebra
H. Bordbar / 2014 / Some properties of closure operation on (Noetherian) BCK-algebra / 12th AHA congress
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