• Communications of the Korean Mathematical Society
• /
• v.12 no.3
• /
• pp.499-505
• /
• 1997

This paper is a continuation of [3]. We prove that if A is quasi-associative (resp. an implicative) ideal of a BCI-algebra X then the k-nil radical of A is a quasi-associative (resp. an implicative) ideal of X. We also construct the quotient algebra $X/[Z;k]$ of a BCI-algebra X by the k-nhil radical [A;k], and show that if A and B are closed ideals of BCI-algebras X and Y respectively, then

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

• East Asian mathematical journal
• /
• v.21 no.2
• /
• pp.171-181
• /
• 2005

In this paper we investigate some more properties of of $S_3$-algebras. We also prove that the class of $S_3$-algebras is contained in the class of commutative BCI-algebras.

• Communications of the Korean Mathematical Society
• /
• v.11 no.3
• /
• pp.601-611
• /
• 1996

In this paper, we introduce the notion of weakly associative BCI-algebras and investigate structure of it. Some of characterizations of elements of the quasi-associative part Q(X) of a BCI-algebra X are shown.

• East Asian mathematical journal
• /
• v.23 no.1
• /
• pp.75-82
• /
• 2007

In this paper we give a concrete computational method to characterize $S_3$-algebras.

• Journal of the Chungcheong Mathematical Society
• /
• v.20 no.3
• /
• pp.279-286
• /
• 2007

Using t-norm T and s-norm S, we introduce the notion of intuitionistic (T, S)-normed fuzzy subalgebra in BCK/BCI-algebra, and some related properties are investigated.

• Communications of the Korean Mathematical Society
• /
• v.17 no.3
• /
• pp.403-407
• /
• 2002

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

• Communications of the Korean Mathematical Society
• /
• v.9 no.3
• /
• pp.531-538
• /
• 1994

This paper is a continuation of [1] and [3]. In [3], the notion of BCI-G parts of BCI-algebras was introduced and various properties were investigated. In this paper, we consider the inverse of [3; Theorem 15], and define a KG-union BCI-algebra and investigate their properties.

• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.3
• /
• pp.399-408
• /
• 2009

A bipolar fuzzy translation and a bipolar fuzzy S-extension of a bipolar fuzzy subalgebra in a BCK/BCI-algebra are introduced, and related properties are investigated.

• Honam Mathematical Journal
• /
• v.32 no.2
• /
• pp.217-226
• /
• 2010

Using the Bu$\c{s}$neag's model ([1, 2, 3]), the notion of pseudo-valuations (valuations) on a ${\mathbf{BCK/BCI}}$-algebra is introduced, and a pseudo-metric is induced by a pseudo-valuation on ${\mathbf{BCK/BCI}}$-algebras. Based on the notion of (pseudo) valuation, we show that the binary operation in ${\mathbf{BCK/BCI}}$-algebras is uniformly continuous.