• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.217-231
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• 2009

The notion of *-medial pseudo BCI-algebras is introduced, and its characterization is discussed. The concepts of associative pseudo ideals (resp. pseudo p-ideals, pseudo q-ideals and pseudo a-ideals) are introduced, and related properties are investigated. Conditions for a pseudo ideal to be a pseudo p-ideal (resp. pseudo q-ideal) are provided. A characterization of an associative pseudo ideal is given. We finally show that every pseudo BCI-homomorphic image and preimage of an associative pseudo ideal (resp. a pseudo p-ideal, a pseudo q-ideal and a pseudo a-ideal) is also an associative pseudo ideal (resp. a pseudo p-ideal, a pseudo q-ideal and a pseudo a-ideal).

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.795-807
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• 2009

The concepts of fuzzy pseudo ideals (resp. fuzzy pseudo p-ideals, associative fuzzy pseudo ideals, fuzzy pseudo q-ideals and fuzzy pseudo a-ideals) in a pseudo BCI-algebra are introduced, and related properties are investigated. Conditions for a fuzzy pseudo ideal to be a fuzzy pseudo p-ideal (resp. fuzzy pseudo q-ideal) are provided. A characterization and properties of an associative fuzzy pseudo ideal are given.

• Journal of applied mathematics & informatics
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• 제12권1_2호
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• pp.243-250
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• 2003

The fuzzification of (Positive implicative) pseudo-ideals in a pseudo-BCK algebra is discussed, and several properties are investigated. Characterizations of a fuzzy pseudo-ideal are displayed.

• Kyungpook Mathematical Journal
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• 제56권1호
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• pp.95-106
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• 2016

As a generalization of Q-algebra, the notion of pseudo Q-algebra is introduced, and some of their properties are investigated. The notions of pseudo subalgebra, pseudo ideal, and pseudo atom in a pseudo Q-algebra are introduced. Characterizations of their properties are provided.

• 호남수학학술지
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• 제37권2호
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• pp.207-219
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• 2015

As a generalization of BH-algebras, the notion of pseudo BH-algebra is introduced, and some of their properties are investigated. The notions of pseudo ideals, pseudo atoms, pseudo strong ideals, and pseudo homomorphisms in pseudo BH-algebras are introduced. Characterizations of their properties are provided. We show that every pseudo homomorphic image and preimage of a pseudo ideal is also a pseudo ideal. Any pseudo ideal of a pseudo BH-algebra can be decomposed into the union of some sets. The notion of pseudo complicated BH-algebra is introduced and some related properties are obtained.

• 충청수학회지
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• 제22권3호
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• pp.333-351
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• 2009

We introduce the concepts of strongly prime fuzzy ideals, powerful fuzzy ideals, strongly primary fuzzy ideals, and pseudo-strongly prime fuzzy ideals of an integral domain R and we provide characterizations of pseudo-valuation domains, almost pseudo-valuation domains, and pseudo-almost valuation domains in terms of these fuzzy ideals.

• 대한수학회보
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• 제58권4호
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• pp.897-908
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• 2021

In this paper, we introduce the notion of pseudo 2-prime ideals in commutative rings. Let R be a commutative ring with a nonzero identity. A proper ideal P of R is said to be a pseudo 2-prime ideal if whenever xy ∈ P for some x, y ∈ R, then x²ⁿ ∈ Pⁿ or y²ⁿ ∈ Pⁿ for some n ∈ ℕ. Various examples and properties of pseudo 2-prime ideals are given. We also characterize pseudo 2-prime ideals of PID's and von Neumann regular rings. Finally, we use pseudo 2-prime ideals to characterize almost valuation domains (AV-domains).

• 대한수학회보
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• 제52권3호
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• pp.935-946
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• 2015

The purpose of this paper is to introduce a new class of rings that is closely related to the classes of pseudo valuation rings (PVRs) and pseudo-almost valuation domains (PAVDs). A commutative ring R is said to be ${\phi}$-ring if its nilradical Nil(R) is both prime and comparable with each principal ideal. The name is derived from the natural map ${\phi}$ from the total quotient ring T(R) to R localized at Nil(R). A prime ideal P of a ${\phi}$-ring R is said to be a ${\phi}$-pseudo-strongly prime ideal if, whenever $x,y{\in}R_{Nil(R)}$ and $(xy){\phi}(P){\subseteq}{\phi}(P)$, then there exists an integer $m{\geqslant}1$ such that either $x^m{\in}{\phi}(R)$ or $y^m{\phi}(P){\subseteq}{\phi}(P)$. If each prime ideal of R is a ${\phi}$-pseudo strongly prime ideal, then we say that R is a ${\phi}$-pseudo-almost valuation ring (${\phi}$-PAVR). Among the properties of ${\phi}$-PAVRs, we show that a quasilocal ${\phi}$-ring R with regular maximal ideal M is a ${\phi}$-PAVR if and only if V = (M : M) is a ${\phi}$-almost chained ring with maximal ideal $\sqrt{MV}$. We also investigate the overrings of a ${\phi}$-PAVR.

• Journal of applied mathematics & informatics
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• 제38권1_2호
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• pp.65-77
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• 2020

In this paper, for any non-empty subsets A, I of a pseudo BCI-algebra X, we introduce the concept of pseudo p-closure of A with respect to I, denoted by A^pc_I, and investigate some related properties. Applying this concept, we state a necessary and sufficient condition for a pseudo BCI-algebra 1) to be a p-semisimple pseudo BCI-algebra; 2) to be a pseudo BCK-algebra. Moreover, we show that A^pc_{0} is the least positive pseudo ideal of X containing A, and characterize it by the union of some branches. We also show that the set of all pseudo ideals of X which A^pc_I = A, is a complete lattice. Finally, we prove that this notion can be used to define a closure operation.

• Kyungpook Mathematical Journal
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• 제55권1호
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• pp.51-62
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• 2015

Pseudo-ŁBCK-algebras are commutative pseudo-BCK-algebras with relative cancellation property. In the paper, we introduce fuzzy prime ideals in pseudo-ŁBCK-algebras and investigate some of their properties. We also give various characterizations of prime ideals and fuzzy prime ideals. Moreover, we present conditions for a pseudo-ŁBCKalgebra to be a pseudo-ŁBCK-chain.