• 충청수학회지
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• 제26권3호
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• pp.453-465
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• 2013

The notion of vague $p$-ideals and vague $a$-ideals of BCI-algebras is introduced, and several properties of them are investigated. We show that a vague set of a BCI-algebra is a vague $a$-ideal if and only if it is both a vague $q$-ideal and a vague $p$-ideal.

• 호남수학학술지
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• 제41권2호
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• pp.285-300
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• 2019

This research focuses on the characterization of an ordered semigroups (OS) in the frame work of generalized bipolar fuzzy interior ideals (BFII). Different classes namely regular, intra-regular, simple and semi-simple ordered semigroups were characterized in term of $({\alpha},{\beta})$-BFII (resp $({\alpha},{\beta})$-bipolar fuzzy ideals (BFI)). It has been proved that the notion of $({\in},{\in}{\gamma}q)$-BFII and $({\in},{\in}{\gamma}q)$-BFI overlap in semi-simple, regular and intra-regular ordered semigroups. The upper and lower part of $({\in},{\in}{\gamma}q)$-BFII are discussed.

• 대한수학회논문집
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• 제25권3호
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• pp.365-372
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• 2010

In this paper, we show that the mapping ${\varphi}(x)\;=\;0*x$ is an endomorphism of a Q-algebra X, which induces a congruence relation "~" such that X/$\varphi$ is a medial Q-algebra. We also study some decompositions of ideals in Q-algebras and obtain equivalent conditions for closed ideals. Moreover, we show that if I is an ideal of a Q-algebra X, then $I^g$ is an ignorable ideal of X.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.419-430
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• 2005

In this paper, we introduce the notions of ($\in,\;{\in} V q$)-fuzzy subnear-ring, ($\in,\;{\in} V q$)-fuzzy ideal and ($\in,\;{\in}V q$)-fuzzy quasi-ideal of near-rings and find more generalized concepts than those introduced by others. The characterization of such ($\in,\;{\in}V q$)-fuzzy ideals are also obtained.

• 대한수학회보
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• 제60권4호
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• pp.1025-1034
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• 2023

Let U be the restricted quantized enveloping algebra Ũ_q(𝖘𝖑₂) over an algebraically closed field of characteristic zero, where q is a primitive 𝑙-th root of unity (with 𝑙 being odd and greater than 1). In this paper we show that any indecomposable submodule of U under the adjoint action is generated by finitely many special elements. Using this result we describe all ideals of U. Moreover, we classify annihilator ideals of simple modules of U by generators.

• 대한수학회논문집
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• 제11권3호
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• pp.563-568
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• 1996

In this paper we study the ramification of prime ideals in the dihedral octic extension N over Q and estimate the possible discriminants of the octic number field N.

• Korean Journal of Mathematics
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• 제28권1호
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• pp.31-47
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• 2020

In this paper, we discuss in detail some of the properties of the new kind of (∈, ∈ ∨q)-fuzzy ideals in Near-ring. The concept of (∈, ∈ ∨q^δ₀)-fuzzy ideal of Near-ring is introduced and some of its related properties are investigated.

• 대한수학회보
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• 제30권1호
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• pp.71-77
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• 1993

Every ring considered in the paper will be assumed to be commutative and have a unit element. An ideal A of a ring R will be called primal if the elements of R which are zero divisors modulo A, form an ideal of R, say pp. If A is a primal ideal of R, P is called the adjoint ideal of A. The adjoint ideal of a primal ideal is prime [2]. The definition of primal ideals may also be formulated as follows: An ideal A of a ring R is primal if in the residue class ring R/A the zero divisors form an ideal of R/A. If Q is a primary idel of a ring R then every zero divisor of R/Q is nilpotent; therefore, Q is a primal ideal of R. That a primal ideal need not be primary, is shown by an example in [2]. Let R[X], and R[[X]] denote the polynomial ring and formal power series ring in an indeterminate X over a ring R, respectively. Let S be a multiplicative system in a ring R and S$^{-1}$ R the quotient ring of R. Let Q be a P-primary ideal of a ring R. Then Q[X] is a P[X]-primary ideal of R[X], and S$^{-1}$ Q is a S$^{-1}$ P-primary ideal of a ring S$^{-1}$ R if S.cap.P=.phi., and Q[[X]] is a P[[X]]-primary ideal of R[[X]] if R is Noetherian [1]. We search for analogous results when primary ideals are replaced with primal ideals. To show an ideal A of a ring R to be primal, it sufficies to show that a-b is a zero divisor modulo A whenever a and b are zero divisors modulo A.

• 대한수학회보
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• 제52권2호
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• pp.525-530
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• 2015

Let D be an integrally closed domain with quotient field K, X be an indeterminate over D, $f=a_0+a_1X+{\cdots}+a_nX^n{\in}D[X]$ be irreducible in K[X], and $Q_f=fK[X]{\cap}D[X]$. In this paper, we show that $Q_f$ is a maximal ideal of D[X] if and only if $(\frac{a_1}{a_0},{\cdots},\frac{a_n}{a_0}){\subseteq}P$ for all nonzero prime ideals P of D; in this case, $Q_f=\frac{1}{a_0}fD[X]$. As a corollary, we have that if D is a Krull domain, then D has infinitely many height-one prime ideals if and only if each maximal ideal of D[X] has height ${\geq}2$.

• East Asian mathematical journal
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• 제18권2호
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• pp.271-282
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• 2002

Let R be a ring with an endomorphism $\sigma$ and a derivation $\delta$. An ideal I of R is ($\sigma,\;\delta$)-ideal of R if $\sigma(I){\subseteq}I$ and $\delta(I){\subseteq}I$. An ideal P of R is a ($\sigma,\;\delta$)-prime ideal of R if P(${\neq}R$) is a ($\sigma,\;\delta$)-ideal and for ($\sigma,\;\delta$)-ideals I and J of R, $IJ{\subseteq}P$ implies that $I{\subseteq}P$ or $J{\subseteq}P$. An ideal Q of R is ($\sigma,\;\delta$)-semiprime ideal of R if Q is a ($\sigma,\;\delta$)-ideal and for ($\sigma,\;\delta$)-ideal I of R, $I^2{\subseteq}Q$ implies that $I{\subseteq}Q$. The ($\sigma,\;\delta$)-prime radical (resp. prime radical) is defined by the intersection of all ($\sigma,\;\delta$)-prime ideals (resp. prime ideals) of R and is denoted by $P_{(\sigma,\delta)}(R)$(resp. P(R)). In this paper, the following results are obtained: (1) $P_{(\sigma,\delta)}(R)$ is the smallest ($\sigma,\;\delta$)-semiprime ideal of R; (2) For every extended endomorphism $\bar{\sigma}$ of $\sigma$, the $\bar{\sigma}$-prime radical of an Ore extension $P(R[x;\sigma,\delta])$ is equal to $P_{\sigma,\delta}(R)[x;\sigma,\delta]$.