• 대한수학회보
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• 제51권1호
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• pp.207-211
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• 2014

The aim of this paper is to prove the next result. Let n > 1 be an integer and let R be a n!-torsion free semiprime ring. Suppose that f : R ${\rightarrow}$ R is an additive mapping satisfying the relation [f(x), $x^n$] = 0 for all $x{\in}R$. Then f is commuting on R.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권4호
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• pp.271-278
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• 2007

Let R be a 2-torsion free semiprime ring. Suppose that there exists a 4-permuting 4-derivation ${\Delta}:R{\times}R{\times}R{\times}R{\rightarrow}R$ such that the trace is centralizing on R. Then the trace of ${\Delta}$ is commuting on R. In particular, if R is a 3!-torsion free prime ring and ${\Delta}$ is nonzero under the same condition, then R is commutative.

• 충청수학회지
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• 제22권3호
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• pp.451-458
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• 2009

Let $n{\geq}2$ be a fixed positive integer and let R be a noncommutative n!-torsion free semiprime ring. Suppose that there exists a symmetric n-derivation $\Delta$ : $R^{n}{\rightarrow}R$ such that the trace of $\Delta$ is centralizing on R. Then the trace is commuting on R. If R is a n!-torsion free prime ring and $\Delta{\neq}0$ under the same condition. Then R is commutative.

• 대한수학회보
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• 제44권4호
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• pp.789-794
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• 2007

Let R be a 3-torsion free semiprime ring and let I be a nonzero two-sided ideal of R. Suppose that there exists a permuting 3-derivation ${\Delta}:R{\times}R{\times}R{\rightarrow}R$ such that the trace is centralizing on I. Then the trace of ${\Delta}$ is commuting on I. In particular, if R is a 3!-torsion free prime ring and ${\Delta}$ is nonzero under the same condition, then R is commutative.

• 대한수학회보
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• 제58권3호
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• pp.659-668
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• 2021

Let R be a semiprime ring with maximal right ring of quotients Q_mr(R), and let n₁, n₂, …, n_k be k fixed positive integers. Suppose that R is (n₁+n₂+⋯+n_k)!-torsion free, and that f : 𝜌 → Q_mr(R) is an additive map, where 𝜌 is a nonzero right ideal of R. It is proved that if [[…[f(x), x^n₁], …], x^n_k] = 0 for all x ∈ 𝜌, then [f(x), x] = 0 for all x ∈ 𝜌. This gives the result of Beidar et al. [2] for semiprime rings. Moreover, it is also proved that if R is p-torsion, where p is a prime integer with p = Σ^k_i=1 n_i and if f : R → Q_mr(R) is an additive map satisfying [[…[f(x), x^n₁], …], x^n_k] = 0 for all x ∈ R, then [f(x), x] = 0 for all x ∈ R.

• Korean Journal of Mathematics
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• 제23권1호
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• pp.37-46
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• 2015

We in this note introduce the concept of semi-IFP rings which is a generalization of IFP rings. We study the basic structure of semi-IFP rings, and construct suitable examples to the situations raised naturally in the process. We also show that the semi-IFP does not go up to polynomial rings.

• 대한수학회논문집
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• 제18권4호
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• pp.629-633
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• 2003

We investigate in this paper rings containing a finitely generated p-injective maximal left ideal. We show that if R is a semiprime ring containing a finitely generated p-injective maximal left ideal, then R is a left p-injective ring. Using this result we are able to give a new characterization of von Neumann regular rings with nonzero socle.

• 대한수학회보
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• 제56권1호
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• pp.23-29
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• 2019

Rings in which all accessible subrings are ideals are called filial. A ring R is called fully filial if all its subrings are filial (that is rings in which the relation of being an ideal is transitive). The present paper is devoted to the study of fully filial torsion rings. We prove a classification theorem for semiprime fully filial torsion rings.

• 대한수학회논문집
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• 제4권1호
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• pp.1-3
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• 1989

• Kyungpook Mathematical Journal
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• 제12권1호
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• pp.19-26
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• 1972