• Communications of the Korean Mathematical Society
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• v.20 no.3
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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.

• Communications of the Korean Mathematical Society
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• v.26 no.3
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• pp.445-454
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• 2011

In this paper, we extend some well known results concerning generalized derivations of prime rings to a generalized (${\sigma}$, ${\tau}$)-derivation.

• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.309-326
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• 2021

In near-ring theory several different types of primitivity exist. These all imply several different types of primeness. In case of near-rings with DCCN most of the types of primeness are known to imply primitivity of a certain kind. We are able to show that also so called 1-prime near-rings imply 1-primitivity. This enables us to classify maximal ideals in near-rings with chain condition with the concept of 1-primeness which leads to further results in the structure theory of near-rings.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.433-445
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• 2016

In the present paper, we expand the domain of work on the concept of semiderivations in 3-prime near-rings through the study of structure and commutativity of near-rings admitting semiderivations satisfying certain differential identities. Moreover, several examples have been provided at places which show that the assumptions in the hypotheses of various theorems are not altogether superfluous.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.409-422
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• 2002

We investigate the relationship between various generalizations of von Neumann regularity condition and the condition that every prime ideal is maximal in exchange rings.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.343-347
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• 2016

Posner's first theorem states that if R is a prime ring of characteristic different from two, $d_1$ and $d_2$ are derivations on R such that the iterate $d_1d_2$ is also a derivation of R, then at least one of $d_1$, $d_2$ is zero. In the present paper we extend this result to *-prime rings of characteristic different from two.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.625-637
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• 2013

We investigate anti-centralizing and skew-centralizing mappings involving generalized derivations and derivations on prime and semiprime rings. We also obtain some range inclusion results for generalized linear derivations and linear derivations on Banach algebras by applying the algebraic techniques. Some results in this note are to improve the ones in [22].

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.1-19
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• 2000

We investigate in this paper the maximality of prime ideals in rings whose simple singular left R-modules are p-injective.

• Kyungpook Mathematical Journal
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• v.45 no.2
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• pp.249-254
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• 2005

Let N be a prime left near-ring with multiplicative center Z and f be a generalized $({\sigma},{\tau})-derivation$ associated with d. We prove commutativity theorems in prime near- rings with generalized $({\sigma},{\tau})-derivation$.

• Honam Mathematical Journal
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• v.29 no.4
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• pp.667-679
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• 2007

We study the prime ideal structure of the direct sum of directed system of rings indexed by a commutative semigroup which is nilpotent extension of a group.