• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.27-36
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• 2006

In this paper, we establish a generalization of fundamental homomorphism theorem in BCK-algebras by using fuzzy BCK-filters. We prove that if ${\mu}$. (resp. v) is a fuzzy BCK-filter of abounded BCK-algebra X (resp. Y), then $\frac{X{\times}Y}{{\mu}{\times}v}{\approxeq}X/{\mu}{\times}Y/v;\;and\;if\;{\mu}$ and F is a BCK-filter in a bounded BCK-algebra X such that $F/{\mu}$ is a BCK-filter of $X/{\mu}$, then $\frac{X/{\mu}}{F/{\mu}}{\approxeq}X/F$.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.265-270
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• 1994

In 1966, Iseki [2] introduced the notion of BCI-algebras which is a generalization of BCK-algebras. Lei and Xi [3] discussed a new class of BCI-algebra, which is called a p-semisimple BCI-algebra. For p-semisimple BCI-algebras, a subalgebra is an ideal. But a subalgebra of an arbitrary BCI/BCK-algebra is not necessarily an ideal. In this note, a BCI/BCK-algebra that every subalgebra is an ideal is called a normal BCI/BCK-algebra, and we give characterizations of normal BCI/BCK-algebras. Moreover we give a positive answer to the problem which is posed in [4].(omitted)

• Kyungpook Mathematical Journal
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• v.46 no.3
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• pp.433-436
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• 2006

In this note we show that a representable difference algebra is equivalent to a commutative BCK-algebra.

• Communications of the Korean Mathematical Society
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• v.30 no.4
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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.

• Communications of the Korean Mathematical Society
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• v.27 no.4
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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 Chungcheong Mathematical Society
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• v.12 no.1
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• pp.15-21
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• 1999

In this paper, we introduce the notion of anti fuzzy prime ideals in a commutative BCK-algebra and obtain some properties of it.

• Communications of the Korean Mathematical Society
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• v.28 no.1
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• pp.11-24
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• 2013

The notion of intersectional soft sets is introduced, and several examples are given. The application of intersectional soft sets to BCK/BCI-algebras is discussed.

• The Mathematical Education
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• v.21 no.3
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• pp.13-14
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• 1983

(1) The direct product (equation omitted) $E_{I}$ of BCK-algebras $E_{I}$, (i=1, 2, 3, …, n), is a BCK-algebra. (2) Let E be a BCK-algebra and $A_1$, $A_1$, …, $A_{n}$ ideals of E. Define a mapping (equation omitted) by the rule f($\chi$)=( $A_1$$\chi$, $A_2$$\chi$, …, $A_{n}$$\chi$). Then f is a homomorphism.ism.ism.

• East Asian mathematical journal
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• v.15 no.1
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• pp.11-17
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• 1999

• East Asian mathematical journal
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• v.21 no.1
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• pp.9-19
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• 2005

In this paper, some properties of intuitionistic fuzzy o-subalgebras of BCK-algebra with condition(S) are investigated.