• Communications of the Korean Mathematical Society
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• v.25 no.2
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• pp.173-184
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• 2010

Using $\cal{N}$-structures, the notion of an $\cal{N}$-ideal in a subtraction algebra is introduced. Characterizations of an $\cal{N}$-ideal are discussed. Conditions for an $\cal{N}$-structure to be an $\cal{N}$-ideal are provided. The description of a created $\cal{N}$-ideal is established.

• Kyungpook Mathematical Journal
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• v.52 no.4
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• pp.375-381
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• 2012

We introduce the concepts of ordered quasi-ideals, ordered bi-ideals in an ordered ternary semigroup and study their properties. Also regular ordered ternary semigroup is defined and several ideal-theoretical characterizations of the regular ordered ternary semigroups are furnished.

• Honam Mathematical Journal
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• v.30 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.47 no.1
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• pp.1-15
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• 2010

We introduce, in this article, the quasi-stable exchange ideal for associative rings. If I is a quasi-stable exchange ideal of a ring R, then so is $M_n$(I) as an ideal of $M_n$(R). As an application, we prove that every square regular matrix over quasi-stable exchange ideal admits a diagonal reduction by quasi invertible matrices. Examples of such ideals are given as well.

• The Pure and Applied Mathematics
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• v.21 no.2
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• pp.105-112
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• 2014

The notion of intersection-soft ideal of CI-algebras is introduced, and related properties are investigated. A characterization of an intersection-soft ideal is provided, and a new intersection-soft ideal from the old one is established.

• Honam Mathematical Journal
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• v.27 no.3
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• pp.353-367
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• 2005

Some properties of the intuitionistic fuzzy (1, 2)-ideal is considered. Characterizations of an intuitionistic fuzzy (1, 2)-ideal are given. We show that every intuitionistic fuzzy (1, 2)-ideal in a group is constant. Using a chain of (1, 2)-ideals of a semigroup S, an intuitionistic fuzzy (1, 2)-ideal of S is established.

• Annals of Fuzzy Mathematics and Informatics
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• v.16 no.3
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• pp.363-371
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• 2018

The main objective of this paper is to connect fuzzy theory, graph theory and fuzzy graph theory with algebraic structure. We introduce the notion of fuzzy graph of semigroup, the notion of fuzzy ideal graph of semigroup as a generalization of fuzzy ideal of semigroup, intuitionistic fuzzy ideal of semigroup, fuzzy graph and graph, the notion of isomorphism of fuzzy graphs of semigroups and regular fuzzy graph of semigroup and we study some of their properties.

• Honam Mathematical Journal
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• v.44 no.2
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• pp.209-218
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• 2022

The notion of positive implicative MBJ-neutosophic ideal of BCK-algebras is defined and some properties of it are investigated. Relations between positive implicative MBJ-neutrosophic ideal and positive implicative ideal are discussed. In a BCK-algebra, the extension property for positive implicative MBJ-neutrosophic ideal is established.

• Korean Journal of Mathematics
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• v.32 no.1
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• pp.121-135
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• 2024

In this paper, we have presented rough ideal statistical convergence of sequence on neutrosophic normed spaces as a significant convergence criterion. As neutrosophication can handle partially dependent components, partially independent components and even independent components involved in real-world problems. By examining some properties related to rough ideal convergence in these spaces we have established some equivalent conditions on the set of ideal statistical limit points for rough ideal statistically convergent sequences.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.2
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• pp.115-119
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• 2007

The notion of ideals in subtraction algebras and characterizations of ideals introduced by Y.B.Jun et al. [?]. Using this idea, we consider the fuzzification of an ideal of a subtraction algebra. In this paper, we define the concept of a fuzzy ideal of a subtraction algebra and study characterizations of a fuzzy ideal. We give some conditions to show that a fuzzy set in a subtraction algebra is a fuzzy ideal of a subtraction algebra. We investigate the generalization of some properties of a fuzzy ideal of a subtraction algebra.