• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.475-489
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• 2006

After the introduction of fuzzy sets by Zadeh [8], there have been a number of generalizations of fundamental concept. The notion of intuitionistic fuzzy sets introduced by Atanassov is one among them. An intuitionistic fuzzy set is also called a bifuzzy set according to [5]. In this paper, we apply the concept of a bifuzzy set to (implicative) ideals in pseudo MV-algebras. The notion of a bifuzzy (implicative) ideal of a pseudo MV-algebra is introduced, and some related properties are investigated. Conditions for a bifuzzy set to be a bifuzzy ideal are given, and characterizations of a bifuzzy (implicative) ideal are provided. Using a family of ideals, bifuzzy ideals are established.

• Journal of applied mathematics & informatics
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• v.37 no.5_6
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• pp.383-397
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• 2019

In this paper, we introduce ${\delta}$-fuzzy ideals in a pseudo complemented distributive lattice in terms of fuzzy filters. It is proved that the set of all ${\delta}$-fuzzy ideals forms a complete distributive lattice. The set of equivalent conditions are given for the class of all ${\delta}$-fuzzy ideals to be a sub-lattice of the fuzzy ideals of L. Moreover, ${\delta}$-fuzzy ideals are characterized in terms of fuzzy congruences.

• Kyungpook Mathematical Journal
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• v.49 no.1
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• pp.183-193
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• 2009

Pseudo-rank functions on Rickart *-rings are introduced and their properties are studied.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.859-870
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• 2015

The notion of quasi-valuation maps based on a subalgebra and an ideal in BCK/BCI-algebras is introduced, and then several properties are investigated. Relations between a quasi-valuation map based on a subalgebra and a quasi-valuation map based on an ideal is established. In a BCI-algebra, a condition for a quasi-valuation map based on an ideal to be a quasi-valuation map based on a subalgebra is provided, and conditions for a real-valued function on a BCK/BCI-algebra to be a quasi-valuation map based on an ideal are discussed. Using the notion of a quasi-valuation map based on an ideal, (pseudo) metric spaces are constructed, and we show that the binary operation * in BCK-algebras is uniformly continuous.

• Korean Journal of Mathematics
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• v.27 no.1
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• pp.131-140
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• 2019

In this paper we have introduced the concept of pseudo-metric which we induced from a pseudo-valuation on KU-algebras and investigated the relationship between pseudo-valuations and ideals of KU-algebras. Conditions for a real-valued function to be a pseudo-valuation on KU-algebras are provided.

• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.281-284
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• 1996

In this paper we characterize strongly prime ideals and prove a theorem: an integral domain R is a PVD if and only if every maximal ideal M of R is strongly prime.

• Kyungpook Mathematical Journal
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• v.57 no.3
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• pp.361-369
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• 2017

A characterization of int-soft ideal is considered, and an int-soft ideal generated by a soft set is discussed. A new int-soft ideal from old one is constructed.

• Korean Journal of Mathematics
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• v.20 no.2
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• pp.185-191
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• 2012

Let D be an integral domain and SF(D) be the set of star operations of finite type on D. We show that if ${\mid}SF(D){\mid}$ < ${\infty}$, then every maximal ideal of D is a $t$-ideal. We give an example of integrally closed quasi-local domains D in which the maximal ideal is divisorial (so a $t$-ideal) but ${\mid}SF(D){\mid}={\infty}$. We also study the integrally closed domains D with ${\mid}SF(D){\mid}{\leq}2$.

• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.1-12
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• 2011

The purpose of this paper is to study pseudo-Riemannian algebras, which are algebras with pseudo-Riemannian non-degenerate symmetric bilinear forms. We nd that pseudo-Riemannian algebras whose left centers are isotropic play a curial role and show that the decomposition of pseudo-Riemannian algebras whose left centers are isotropic into indecomposable non-degenerate ideals is unique up to a special automorphism. Furthermore, if the left center equals the center, the orthogonal decomposition of any pseudo-Riemannian algebra into indecomposable non-degenerate ideals is unique up to an isometry.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1095-1106
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• 2020

The purpose of this paper is to introduce a new class of rings that is closely related to the class of pseudo-Krull domains. Let 𝓗 = {R | R is a commutative ring and Nil(R) is a divided prime ideal of R}. Let R ∈ 𝓗 be a ring with total quotient ring T(R) and define 𝜙 : T(R) → R_Nil(R) by ${\phi}({\frac{a}{b}})={\frac{a}{b}}$ for any a ∈ R and any regular element b of R. Then 𝜙 is a ring homomorphism from T(R) into R_Nil(R) and 𝜙 restricted to R is also a ring homomorphism from R into R_Nil(R) given by ${\phi}(x)={\frac{x}{1}}$ for every x ∈ R. We say that R is a 𝜙-pseudo-Krull ring if 𝜙(R) = ∩ R_i, where each R_i is a nonnil-Noetherian 𝜙-pseudo valuation overring of 𝜙(R) and for every non-nilpotent element x ∈ R, 𝜙(x) is a unit in all but finitely many R_i. We show that the theories of 𝜙-pseudo Krull rings resemble those of pseudo-Krull domains.