• 대한수학회논문집
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• 제25권1호
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• pp.1-9
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• 2010

In this note, we introduce a permuting 3-derivation in nearrings and investigate the conditions for a near-ring to be a commutative ring.

• 대한수학회논문집
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• 제20권3호
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• pp.457-466
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• 2005

We study in this note rings whose prime radicals are completely prime. We obtain equivalent conditions to the complete 2-primal-ness and observe properties of completely 2-primal rings, finding examples and counterexamples to the situations that occur naturally in the process.

• 대한수학회논문집
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• 제19권2호
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• pp.211-217
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• 2004

In a ring $R_n(K,\;J)$ where K is a commutative ring with identity and J is an ideal of K, all prime ideals of $R_n(K,\;J)$ are of the form either $M_n(P)\;o;R_n(P,\;P\;{\cap}\;J)$. Therefore there is a one to one correspondence between prime ideals of K not containing J and prime ideals of $R_n(K,\;J)$.

• 대한수학회보
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• 제47권5호
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• pp.1077-1087
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• 2010

Anderson-Smith [1] studied weakly prime ideals for a commutative ring with identity. Blair-Tsutsui [2] studied the structure of a ring in which every ideal is prime. In this paper we investigate the structure of rings, not necessarily commutative, in which all ideals are weakly prime.

• 충청수학회지
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• 제7권1호
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• pp.87-95
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• 1994

Relationships between the prime ideals of a ring R and of a normalizing extension S have been studied by several authors. Relationships between the prime ideals of a ring R and of an intermediate normalizing extension T also have studied by several authors where $R{\subset}T{\subset}S$. In this note, some relationships between prime ideals of T and S are studied.

• 호남수학학술지
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• 제40권2호
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• pp.219-225
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• 2018

In this paper, we characterize the prime submodules of an injective module over a Noetherian ring.

• 대한수학회논문집
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• 제18권4호
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• pp.615-620
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• 2003

Semi-meet-prime projective modules and fully invariant meet-prime submodules of a projective module are studied. Actually a generalization of the Schur's lemma and semi-prime endmorphism rings of projective modules are considered.

• 대한수학회보
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• 제56권1호
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• pp.103-110
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• 2019

In this paper, we give a characterization of prime submodules of an injective module over a Noetherian ring.

• 대한수학회보
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• 제61권2호
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• pp.335-353
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• 2024

The objective of this paper is to study some central identities involving generalized derivations and anti-automorphisms in prime rings. Using the tools of the theory of functional identities, several known results have been generalized as well as improved.

• 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.