• Communications of the Korean Mathematical Society
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• 제30권4호
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• pp.385-402
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• 2015

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.

• The Pure and Applied Mathematics
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• 제30권4호
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• pp.429-442
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• 2023

In this paper, we introduce the concept of fuzzy ideals, anti-fuzzy ideals of Γ-BCK-algebras. We study the properties of fuzzy ideals, anti-fuzzy ideals of Γ-BCK-algebras. We prove that if f^-1(µ) is a fuzzy ideal of M, then µ is a fuzzy ideal of N, where f : M → N is an epimorphism of Γ-BCK-algebras M and N.

• Communications of the Korean Mathematical Society
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• 제8권2호
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• pp.225-231
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• 1993

• East Asian mathematical journal
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• 제15권1호
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• pp.11-17
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• 1999

• Communications of the Korean Mathematical Society
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• 제10권3호
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• pp.499-518
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• 1995

In this paper we consider more systematically the centralizer C(S) of the set $S = {f_a $\mid$ f_a : X \to X ; x \longmapsto x * a, a \in X}$ with respect to the semigroup End(X) of all endomorphisms of an implicative BCK-algebra X with the condition (S). We obtain a series of interesting results. The main results are stated as follows : (1) C(S) with repect to a binary operation * defined in a certain way forms a bounded implicative BCK-algebra with the condition (S). (2) X can be imbedded in C(S) such that X is an ideal of C(S)/ (3) If X is not bounded, it can be imbedded in a bounded subalgebra T of C(S) such that X is a maximal ideal of T. (4) If $X (\neq {0})$ is semisimple, C(S) is BCK-isomorphic to $\prod_{i \in I}{A_i}$ in which ${A_i}_{i \in I}$ is simple ideal family of X.

• Korean Journal of Fisheries and Aquatic Sciences
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• 제34권2호
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• pp.145-150
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• 2001

A marine bacterium having a high oil-degrading activity was isolated from the coastal water of Yosu, Korea, identified as Pseudomonas sp. and named Pseudomonas sp. BCK-1. The optimal temperature, pH and NaCl concentration for cell growth was $30^{\circ}C$, 7.0 and $3\%$ (w/v), respectively. After cultivation at $30^{\circ}C$, 180 rpm in 250 mL erlenmeyer flask for 72 and 168 hours, $2\%$ (w/v) arabian light crude oil (ACO) and bunker C oil (BCO) which are considered to be hardly biodegradable compounds were degraded $92\%$ (w/w) and $72\%$ (w/w), respectively.

• Communications of the Korean Mathematical Society
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• 제24권3호
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• pp.361-366
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• 2009

In this paper we consider constructive function triples on the real numbers $\mathbb{R}$ and on (not necessarily commutative) integral domains D which permit the construction of a multitude of d-algebras via these constructive function triples. At the same time these constructions permit one to consider various conditions on these d-algebras for subsets of solutions of various equations, thereby producing geometric problems and interesting visualizations of some of these subsets of solutions. In particular, one may consider what notions such as "locally BCK" ought to mean, certainly in the setting provided below.

• Communications of the Korean Mathematical Society
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• 제27권4호
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• pp.645-651
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• 2012

Based on a sub-BCK-algebra K of a BCI-algebra X, the notions of N-subalgebras and N-ideals of X are introduced, and their relations/properties are investigated.

• Journal of the Korean Institute of Intelligent Systems
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• 제12권2호
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• pp.182-186
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• 2002

We investigate the quotient structure of a product BCK-algebra and fundamental homomorphism theorem and show their some properties.

• Journal of applied mathematics & informatics
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• 제8권1호
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• pp.261-272
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• 2001

The intuitionistic fuzzification of a subalgebra in a BCK/BCI-algebra is considered, and related results are investigated. The notion of equivalence relations on the family of all intuitionistic fuzzy subalgebras of a BCK/BCI-algebra is introduced, and then some properties are discussed.