• Bulletin of the Korean Mathematical Society
• /
• v.39 no.3
• /
• pp.485-494
• /
• 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.

• Communications of the Korean Mathematical Society
• /
• v.18 no.4
• /
• pp.615-620
• /
• 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
• /
• v.46 no.2
• /
• pp.153-167
• /
• 2006

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

• East Asian mathematical journal
• /
• v.19 no.2
• /
• pp.233-240
• /
• 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
• /
• v.21 no.1
• /
• pp.1-7
• /
• 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 $d\sigma={\sigma}d,\;d\tau={\tau}d$.

• Journal of the Chungcheong Mathematical Society
• /
• v.2 no.1
• /
• pp.37-44
• /
• 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
• /
• v.6 no.1
• /
• pp.239-246
• /
• 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.

• Journal of Applied and Pure Mathematics
• /
• v.6 no.3_4
• /
• pp.155-165
• /
• 2024

Let R be a semi-prime ring. Let [δ₁, D₁] and [δ₂, D₂] be two generalized symmetric reverse biderivations of R with associated reverse biderivations D₁ and D₂. The main aim of the present paper is to establish conditions of orthogonality for symmetric reverse biderivations and symmetric generalized reverse biderivations in R.

• Communications of the Korean Mathematical Society
• /
• v.36 no.4
• /
• pp.641-650
• /
• 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.

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