• East Asian mathematical journal
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• 제24권2호
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• pp.187-190
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• 2008

As a generalization of BCI-algebras, the notion of pseudo-BCI algebras is introduced, and some of their properties are investigated. Characterizations of pseudo-BCI algebras are established. Some conditions for a pseudo-BCI algebra to be a pseudo-BCK algebra are given.

• Journal of applied mathematics & informatics
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• 제33권5_6호
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• pp.671-686
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• 2015

The notion of soft α-ideals and α-idealistic soft BCI-algebras is introduced and their basic properties are discussed. Relations between soft ideals and soft α-ideals of soft BCI-algebras are provided. Also idealistic soft BCI-algebras and α-idealistic soft BCI-algebras are being related. The restricted intersection, union, restricted union, restricted difference and "AND" operation of soft α-ideals and α-idealistic soft BCI-algebras are established. The characterizations of (fuzzy) α-ideals in BCI-algebras are given by using the concept of soft sets. Relations between fuzzy α-ideals and α-idealistic soft BCI-algebras are discussed.

• 대한수학회논문집
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• 제9권2호
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• pp.275-278
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• 1994

In 1966, Iseki [4] introduced the notion of BCI-algebras which is a generalization of BCK-algebras. The ideal theory plays an important role in studying BCK/BCI-algebras. In this paper we study decompositions of ideals in BCI-algebras, and give a characterization of closed ideals. Also we define ignorable ideals in BCI-algebras, and investigates its properties.(omitted)

• 대한수학회논문집
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• 제9권2호
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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)

• 호남수학학술지
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• 제29권2호
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• pp.289-297
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• 2007

In this paper, we show that BCI-algebras P and Q are injective if and only if its direct sum P $\oplus$ Q is injective. Moreover, we obtain the equivalent conditions for a p-semisimple BCI-algebra to be p-injective.

• 대한수학회보
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• 제41권1호
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• pp.167-179
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• 2004

The notions of FSI-ideals and FSC-ideals in BCI-algebras are introduced. The characterization properties of FSI-ideals and FSC-ideals are obtained. We investigate the relations between FSI-ideals (resp. FSC-ideals) and other fuzzy ideals, between FSI-ideals (resp. FSC-ideals) and BCI-algebras, and show that a fuzzy subset of a BCI-algebra is an FSI-ideal if and only if it is both an FSC-ideal and a fuzzy BCI-positive implicative ideal.

• 대한수학회논문집
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• 제24권3호
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• pp.321-331
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• 2009

In this paper, we investigate some fundamental properties and establish some results of f-derivations of BCI-algebras. Also, we prove Der(X), the collection of all f-derivations, form a semigroup under certain binary operation.

• 대한수학회논문집
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• 제10권4호
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• pp.815-821
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• 1995

We introduce the concept of weakly positive implicative ideals in BCI-algebras and give some characterization of weakly positive implicative BCI-algebras and weakly positive implicative ideals.

• 대한수학회논문집
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• 제10권2호
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• pp.269-273
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• 1995

In this paper, we introduce the notion of $\lambda$-associative BCI-algebras, investigate important properties of such algebras, and discuss the structure of it.

• 대한수학회논문집
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• 제17권3호
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• pp.403-407
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• 2002

In this note We discuss the Uniformity in BCI-algebras using Zhang's congruence relation.