• 대한수학회보
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• 제58권3호
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• pp.711-720
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• 2021

Let R denote a commutative noetherian ring, and let 𝐱 := x1, …, xd be an R-regular sequence. Suppose that 𝖆 denotes a monomial ideal with respect to 𝐱. The first purpose of this article is to show that 𝖆 is irreducible if and only if 𝖆 is a generalized-parametric ideal. Next, it is shown that, for any integer n ≥ 1, (x1, …, xd)n = ⋂P(f), where the intersection (irredundant) is taken over all monomials f = xe11 ⋯ xedd such that deg(f) = n - 1 and P(f) := (xe1+11, ⋯, xed+1d). The second main result of this paper shows that if 𝖖 := (𝐱) is a prime ideal of R which is contained in the Jacobson radical of R and R is 𝖖-adically complete, then 𝖆 is a parameter ideal if and only if 𝖆 is a monomial irreducible ideal and Rad(𝖆) = 𝖖. In addition, if a is generated by monomials m1, …, mr, then Rad(𝖆), the radical of a, is also monomial and Rad(𝖆) = (ω1, …, ωr), where ωi = rad(mi) for all i = 1, …, r.

• 충청수학회지
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• 제29권4호
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• pp.523-530
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• 2016

Let R be a 3!-torsion free semiprime ring, and let $D:R{\rightarrow}R$ be a Jordan derivation on a semiprime ring R. In this case, we show that [D(x), x]D(x) = 0 if and only if D(x)[D(x), x] = 0 for every $x{\in}R$. In particular, let A be a Banach algebra with rad(A). If D is a continuous linear Jordan derivation on A, then we see that $[D(x),x]D(x){\in}rad(A)$ if and only if $[D(x),x]D(x){\in}rad(A)$ for all $x{\in}A$.

• 충청수학회지
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• 제29권4호
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• pp.531-542
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• 2016

Let R be a 3!-torsion free noncommutative semiprime ring, and suppose there exists a Jordan derivation $D:R{\rightarrow}R$ such that [[D(x),x], x]D(x) = 0 or D(x)[[D(x), x], x] = 0 for all $x{\in}R$. In this case we have $[D(x),x]^3=0$ for all $x{\in}R$. Let A be a noncommutative Banach algebra. Suppose there exists a continuous linear Jordan derivation $D:A{\rightarrow}A$ such that $[[D(x),x],x]D(x){\in}rad(A)$ or $D(x)[[D(x),x],x]{\in}rad(A)$ for all $x{\in}A$. In this case, we show that $D(A){\subseteq}rad(A)$.

• 대한수학회지
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• 제55권5호
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• pp.1031-1043
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• 2018

Let R be a commutative ring with $1{\neq}0$, I a proper ideal of R, and m and n positive integers. In this paper, we define I to be a weakly (m, n)-closed ideal if $0{\neq}x^m\;{\in}I$ for $x{\in}R$ implies $x^n{\in}I$, and R to be an (m, n)-von Neumann regular ring if for every $x{\in}R$, there is an $r{\in}R$ such that $x^mr=x^n$. A number of results concerning weakly(m, n)-closed ideals and (m, n)-von Neumann regular rings are given.

• 대한수학회지
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• 제42권5호
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• pp.1003-1015
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• 2005

Klein proved that polynomial rings over nil rings of bounded index are also nil of bounded index; while Puczylowski and Smoktunowicz described the nilradical of a power series ring with an indeterminate. We extend these results to those with any set of commuting indeterminates. We also study prime radicals of power series rings over some class of rings containing the case of bounded index, finding some examples which elaborate our arguments; and we prove that R is a PI ring of bounded index then the power series ring R[[X]], with X any set of indeterminates over R, is also a PI ring of bounded index, obtaining the Klein's result for polynomial rings as a corollary.

• 대한수학회보
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• 제51권2호
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• pp.579-594
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• 2014

Let R be a ring and $Nil_*$(R) be the prime radical of R. In this paper, we say that a ring R is left $Nil_*$-coherent if $Nil_*$(R) is coherent as a left R-module. The concept is introduced as the generalization of left J-coherent rings and semiprime rings. Some properties of $Nil_*$-coherent rings are also studied in terms of N-injective modules and N-flat modules.

• 호남수학학술지
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• 제29권4호
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• pp.555-567
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• 2007

We first find strongly 2-primal rings whose sub direct product is not (strongly) 2-primal. Moreover we observe some kinds of ring extensions of (strongly) 2-primal rings. As an example we show that if R is a ring and M is a multiplicative monoid in R consisting of central regular elements, then R is strongly 2-primal if and only if so is $RM^{-1}$. Various properties of (strongly) 2-primal rings are also studied.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권4호
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• pp.347-375
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• 2016

Let R be a 3!-torsion free noncommutative semiprime ring, U a Lie ideal of R, and let $D:R{\rightarrow}R$ be a Jordan derivation. If [D(x), x]D(x) = 0 for all $x{\in}U$, then D(x)[D(x), x]y - yD(x)[D(x), x] = 0 for all $x,y{\in}U$. And also, if D(x)[D(x), x] = 0 for all $x{\in}U$, then [D(x), x]D(x)y - y[D(x), x]D(x) = 0 for all $x,y{\in}U$. And we shall give their applications in Banach algebras.

• Journal of applied mathematics & informatics
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• 제7권3호
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• pp.995-1004
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• 2000

In this paper we shall give a slight generalization of J. Vukman's Theorem. And show from the result that the image of a continuous linear Jordan derivation on a noncommutative Banach algebra A is contained in the radical under the condition [D(x),x]E(x) ${\in}$ rad(A) for all $x{\in}A$ . And we show some properties of the derivations on noncommutative Banach algebras.

• 반도체디스플레이기술학회지
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• 제10권1호
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• pp.75-81
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• 2011

Today, FPD manufactures are eager to develop larger and larger glass to become the prime market leader. To follow this need, larger AMHS(Automated Material Handling System) development is essential. The radical increase of glass/cassette weight puts a lot of pressure on stocker robot's dual arms, which can cause a damage of expensive glasses and contaminate a clean room facility. In this paper the axiomatic design method is used to institute a design guideline to evenly distribute a pressure throughout the stocker robot structure.