• 대한수학회보
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• 제39권3호
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• pp.485-494
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• 2002

In this paper we will show that if there exist derivations D, G on a n!-torsion free semi-prime ring R such that the mapping $D^2+G$ is n-commuting on R, then D and G are both commuting on R. And we shall give the algebraic conditions on a ring that a Jordan derivation is zero.

• 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.

• Kyungpook Mathematical Journal
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• 제46권2호
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• pp.153-167
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• 2006

We study permuting tri-derivations in ${\Gamma}$-rings and give an example.

• 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

• East Asian mathematical journal
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• 제21권1호
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• pp.1-7
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• 2005

The object of this paper is to study($\sigma,\;\tau$)-Lie ideals in semi-prime rings with derivation. Main result is the following theorem: Let R be a semi-prime ring with 2-torsion free, $\sigma$ and $\tau$ two automorphisms of R such that $\sigma\tau=\tau\sigma$=, U be both a non-zero ($\sigma,\;\tau$)-Lie ideal and subring of R. If $d^2(U)=0$, then d(U)=0 where d a non-zero derivation of R such that $d\sigma={\sigma}d,\;d\tau={\tau}d$.

• 충청수학회지
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• 제2권1호
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• pp.37-44
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• 1989

In this paper, it is shown that automatic continuity of derivations on some semi prime Banach algebras can be extended to higher derivations. In particular, we show that if every prime ideal is closed in a commutative semi prime Banach algebra then every higher derivation on it is continuous.

• Journal of applied mathematics & informatics
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• 제6권1호
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• pp.239-246
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• 1999

The purpose of this paper is to prove the following result: Let R be a 2-torsion free noncommutative semi-prime ring and D:RlongrightarrowR a derivation. Suppose that $[[D(\chi),\chi],\chi]\in$ Z(R) holds for all $\chi \in R$. Then D is commuting on R.

• 대한수학회논문집
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• 제36권4호
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• pp.641-650
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• 2021

The notions of skew-commuting/commuting/semi-commuting/skew-centralizing/semi-centralizing mappings play an important role in ring theory. ${\mathfrak{C}}^*$-algebras with these properties have been studied considerably less and the existing results are motivating the researchers. This article elaborates the structure of prime rings and ${\mathfrak{C}}^*$-algebras satisfying certain functional identities involving automorphisms.

• 호남수학학술지
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• 제29권4호
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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.

• 대한수학회지
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• 제50권6호
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• pp.1183-1198
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• 2013

We will introduce and study the notion of prime bases for weakly prime submodules and utilize them to derive some formulas on the weak radical of submodules of a module. In particular, we will show that every one dimensional integral domain weakly satisfies the radical formula and state some necessary conditions on local integral domains which are semi-compatible or satisfy the radical formula and also on Noetherian rings which weakly satisfy the radical formula.