• 호남수학학술지
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• 제28권4호
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• pp.485-497
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• 2006

Further properties on a fuzzy ideal of a right K(G)-algbera $\mathcal{G}$ are investigated. Using a family of ideals of a right K(G)-algebra $\mathcal{G}$ with additional conditions, a fuzzy ideal of $\mathcal{G}$ is established. Given a fuzzy set $\mu$ in $\mathcal{G}$, the least fuzzy ideal of $\mathcal{G}$ containing $\mu$ is described. Using a chain of ideals of $\mathcal{G}$, a fuzzy ideal of $\mathcal{G}$ is constructed, and their properties are investigated.

• Kyungpook Mathematical Journal
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• 제46권2호
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• pp.181-184
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• 2006

We prove the following results: (1) Let R be a strongly euclidean semiring. Then an ideal A of $R_{n{\times}n}$ is a partitioning ideal if and only if it is a subtractive ideal. (2) A monic ideal M of R[$x$], where R is a strongly euclidean semiring, is a partitioning ideal if and only if it is a subtractive ideal.

• 대한수학회보
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• 제35권1호
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• pp.13-24
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• 1998

We define an LI-ideal of a lattice implication algebra and show that every LI-ideal is a lattice ideal. We give an exampl that a lattice ideal may not be an LI-ideal, and show that every lattice ideal is an LI-ideal in a lattice H implication algebra. we discuss the relationship between filters and LI-ideals, and study how to generate an LI-ideal by a set. We construct the quotient structure by using an LI-ideal, and study the properties of LI-ideals related to implication homomorphisms.

• Korean Journal of Mathematics
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• 제8권1호
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• pp.87-90
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• 2000

Let R be an integral domain with identity. We show that each associated prime ideal of a principal ideal in R[X] has height one if and only if each associated prime ideal of a principal ideal in R has height one and R is an S-domain.

• East Asian mathematical journal
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• 제18권1호
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• pp.155-162
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• 2002

Lajos([1-3]) gave the ideal-theoretical characterizations of some classes of semigroups without "order". The first author([4]) gave the ideal-theoretical characterization of some classes of po-semigroup with order $"{\leq}"$. In this paper we give the other characterizations.

• Kyungpook Mathematical Journal
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• 제46권3호
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• pp.357-365
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• 2006

This paper is a sequel of our previous paper [1]. In this paper, we introduce the notions of regular ideal and partial ideal ($p$-ideal) in a ternary semiring and using these two notions we characterize regular ternary semiring.

• 호남수학학술지
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• 제36권3호
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• pp.555-568
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• 2014

On the basis of the theory of a falling shadow and fuzzy sets, the notion of a falling fuzzy BCI-commutative ideal of a BCI-algebra is introduced. Relations between falling fuzzy BCI-commutative ideals and falling fuzzy ideals are given. Relations between fuzzy BCI-commutative ideals and falling fuzzy BCI-commutative ideals are provided. Characterizations of a falling fuzzy BCI-commutative ideal are established, and conditions for a falling fuzzy (closed) ideal to be a falling fuzzy BCI-commutative ideal are considered.

• 대한수학회보
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• 제39권2호
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• pp.185-198
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• 2002

We Consider the fuzzification of sub-implicative ideals in BCI-algebras, and investigate some related properties. We give conditions for a fuzzy ideal to be a fuzzy sub-implicative ideal. we show that (1) every fuzzy sub-implicative ideal is a fuzzy ideal, but the converse is not true, (2) every fuzzy sub-implicative ideal is a fuzzy positive implicative ideal, but the converse is not true, and (3) every fuzzy p-ideal is a fuzzy sub-implicative ideal, but the converse is not true. Using a family of sub-implicative ideals of a BCI-algebra, we establish a fuzzy sub-implicative ideal, and using a level set of a fuzzy set in a BCI-algebra, we give a characterization of a fuzzy sub-implicative ideal.

• 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.

• 호남수학학술지
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• 제30권1호
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• pp.65-74
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• 2008

The notion of vague quick ideals of BCK/BCI-algebras is introduced, and several properties are investigated. Relations between a vague ideal, a vague BCK/BCI-algebra and a vague quick ideal are provided. A condition for a vague quick ideal to be a vague ideal is given.