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SEMI-PRIME CLOSURE OPERATIONS ON BCK-ALGEBRA
BORDBAR, HASHEM,ZAHEDI, MOHAMMAD MEHDI Korean Mathematical Society 2015 대한수학회논문집 Vol.30 No.4
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.
Neutrosophic falling shadows applied to subalgebras and ideals in $BCK/BCI$-algebras
전영배,Florentin Smarandache,Hashem Bordbar 원광대학교 기초자연과학연구소 2018 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.15 No.3
As a combination of neutrosophic set and falling shadow, neutrosophic falling shadow is introduced, and applied to $BCK/BCI$-algebras. Falling neutrosophic subalgebra and falling neutrosophic ideal in $BCK/BCI$-algebras are introduced, and related properties are investigated. Relations between falling neutrosophic subalgebra and falling neutrosophic ideal are discussed. A characterization of falling neutrosophic ideal is established.
UNI-SOFT COMMUTATIVE IDEALS WITH THRESHOLDS IN BCK/BCI-ALGEBRAS
Jun, Young Bae,Lee, Kyoung Ja,Bordbar, Hashem,Song, Seok-Zun The Honam Mathematical Society 2018 호남수학학술지 Vol.40 No.3
The notion of a uni-soft commutative ideal with thresholds is introduced, and related properties are investigated. Relations between a uni-soft ideal with thresholds and a uni-soft commutative ideal with thresholds are discussed. Conditions for a uni-soft ideal with thresholds to be a uni-soft commutative ideal with the same thresholds are provided. Characterizations of a uni-soft commutative ideal with thresholds are established.
UNI-SOFT COMMUTATIVE IDEALS WITH THRESHOLDS IN BCK=BCI-ALGEBRAS
( Young Bae Jun ),( Kyoung Ja Lee ),( Hashem Bordbar ),( Seok-zun Song ) 호남수학회 2018 호남수학학술지 Vol.40 No.3
The notion of a uni-soft commutative ideal with thresholds is introduced, and related properties are investigated. Relations between a uni-soft ideal with thresholds and a uni-soft commutative ideal with thresholds are discussed. Conditions for a unisoft ideal with thresholds to be a uni-soft commutative ideal with the same thresholds are provided. Characterizations of a uni-soft commutative ideal with thresholds are established.