• 대한수학회논문집
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• 제11권3호
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• pp.569-573
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• 1996

We study some special cases of Chow groups of a ramified complete regular local ring R of dimension n. We prove that (a) for codimension 3 Gorenstein ideal I, [I] = 0 in $A_{n-3}(R)$ and (b) for a particular class of almost complete intersection prime ideals P of height i, [P] = 0 in $A_{n-i}(R)$.

• East Asian mathematical journal
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• 제19권2호
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• pp.233-240
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• 2003

Xie and Wu introduced an m-system in a po-semigroup. Kehayopulu gave characterizations of weakly prime ideals of po-semigroups and Lee and Kwon add two characterizations for weakly prime ideals. In this paper, we give a characterization of weakly prime ideals and a characterization of weakly semi-prime ideals in po-semigroups using m-system and n-system, respectively

• 호남수학학술지
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• 제45권4호
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• pp.678-681
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• 2023

Let G be a cyclic group of prime power order p^k, and let I be the augmentation ideal of the integral group ring ℤ[G]. We define a derivation on ℤ/p^kℤ[G], and show that for 2 ≤ n ≤ p, an element α ∈ I is in Iⁿ if and only if the i-th derivative of the image of α in ℤ/p^kℤ[G] vanishes for 1 ≤ i ≤ (n - 1).

• 대한수학회보
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• 제57권1호
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• pp.117-126
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• 2020

Let R be a commutative ring with identity. A proper ideal I of R is called 2-prime if for all a, b ∈ R such that ab ∈ I, then either a² or b² lies in I. In this paper, we study 2-prime ideals which are generalization of prime ideals. Our study provides an analogous to the prime avoidance theorem and some applications of this theorem. Also, it is shown that if R is a PID, then the families of primary ideals and 2-prime ideals of R are identical. Moreover, a number of examples concerning 2-prime ideals are given. Finally, rings in which every 2-prime ideal is a prime ideal are investigated.

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.455-464
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• 2006

In this paper, we introduce the concept of an interval-valued fuzzy left (right, two-sided, interior, bi-) ideal generated by an interval-valued fuzzy subset in semigroups. Some characterizations of such generated interval-valued fuzzy ideals are also discussed.

• East Asian mathematical journal
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• 제28권3호
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• pp.281-285
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• 2012

In this paper, the concept of *-prime ideals in non-associative near-rings is introduced and then will be studied. For this purpose, first we introduce the notions of *-operation, *-prime ideal and *-system in a near-ring. Next, we will define the *-sequence, *-strongly nilpotent *-prime radical of near-rings, and then obtain some characterizations of *-prime ideal and *-prime radical $r_s$(I) of an ideal I of near-ring N.

• 대한수학회지
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• 제39권1호
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• pp.127-135
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• 2002

Let I be an ideal in a Gorenstein local ring A with the maximal ideal m. Then we say that I is an equimultiple good ideal in A, if I contains a reduction Q = ( $a_1$, $a_2$,ㆍㆍㆍ, $a_{s}$ ) generated by s elements in A and G(I) =(equation omitted)$_{n 0}$ $I^{n}$ / $I^{n＋1}$ of I is a Gorenstein ring with a(G(I)) = 1 - s, where s = h $t_{A}$ I and a(G(I)) denotes the a-invariant of G(I). Let $X_{A}$$^{s}$ denote the set of equimultiple good ideals I in A with h $t_{A}$ I = s, R(I) = A [It] be the Rees algebra of I, and $K_{R(I)}$ denote the canonical module of R(I). Let a I such that $I^{n＋l}$ = a $I^{n}$ for some n$\geq$0 and $\mu$$_{A}$(I)$\geq$2, where $\mu$$_{A}$(I) denotes the number of elements in a minimal system of generators of I. Assume that A/I is a Cohen-Macaulay ring. We show that the following conditions are equivalent. (1) $K_{R(I)}$(equation omitted)R(I)＋as graded R(I)-modules. (2) $I^2$ = aI and aA : I$\in$ $X^1$$_{A}$._{A}$./.

• Korean Journal of Mathematics
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• 제4권1호
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• pp.45-49
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• 1996

Let $F_0$ be the maximal real subfield of $\mathbb{Q}({\zeta}_q+{\zeta}_q^{-1})$ and $F_{\infty}={\cup}_{n{\geq}0}F_n$ be its basic $\mathbb{Z}_p$-extension. Let $A_n$ be the Sylow $p$-subgroup of the ideal class group of $F_n$. The aim of this paper is to examine the injectivity of the natural $mapA_n{\rightarrow}A_m$ induced by the inclusion $F_n{\rightarrow}F_m$ when $m>n{\geq}0$. By using cyclotomic units of $F_n$ and by applying cohomology theory, one gets the following result: If $p$ does not divide the order of $A_1$, then $A_n{\rightarrow}A_m$ is injective for all $m>n{\geq}0$.

• 호남수학학술지
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• 제36권4호
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• pp.863-884
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• 2014

In this paper, we introduce a coupled $\mathcal{N}$-structure which is the generalization of $\mathcal{N}$-structure. Using this coupled $\mathcal{N}$-structure, we have applied in a subtraction algebra and have introduced the notion of a coupled $\mathcal{N}$-subalgebra, a coupled $\mathcal{N}$-ideal. Also the characterization of coupled $\mathcal{N}$-ideal is presented.

• 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 ${\geq}2$.