• Journal of the Chungcheong Mathematical Society
• /
• v.29 no.3
• /
• pp.443-451
• /
• 2016

In this paper, we introduce the concept of a symmetric bi-f-multiplier in incline algebras and give some properties of incline algebras. Also, we characterize Ker(D) and $Fix_a(D)$ by symmetric bi-f-multipliers in incline algebras.

• Journal of the Chungcheong Mathematical Society
• /
• v.35 no.2
• /
• pp.125-136
• /
• 2022

The goal of this paper is to introduce the notion of generalized symmetric bi-f-derivations in lattices and to study some properties of generalized symmetric f-derivations of lattice. Moreover, we consider generalized isotone symmetric bi-f-derivations and fixed sets related to generalized symmetric bi-f-derivations.

• Bulletin of the Korean Mathematical Society
• /
• v.44 no.4
• /
• pp.789-794
• /
• 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.

• East Asian mathematical journal
• /
• v.15 no.1
• /
• pp.105-109
• /
• 1999

• Bulletin of the Korean Mathematical Society
• /
• v.43 no.1
• /
• pp.9-16
• /
• 2006

The purpose of this paper is to define the symmetric $bi-(\sigma,\;\tau)$ derivations on prime and semi prime Gamma rings and to prove some results concerning symmetric $bi-(\sigma,\;\tau)$derivations on prime and semi prime Gamma rings.

• Kyungpook Mathematical Journal
• /
• v.46 no.2
• /
• pp.153-167
• /
• 2006

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

• Journal of applied mathematics & informatics
• /
• v.5 no.3
• /
• pp.819-826
• /
• 1998

The purpose of this paper is to prove the following results; (1) Let R be a prime ring of char $(R)\neq 2$ and I a nonzero left ideal of R. The existence of a nonzero symmetric bi-derivation D : $R\timesR\;\longrightarrow\;$ such that d is sew-commuting on I where d is the trace of D forces R to be commutative (2) Let m and n be integers with $m\;\neq\;0.\;or\;n\neq\;0$. Let R be a noncommutative prime ring of char$ (R))\neq \; 2-1\; p_1 \;n_1$ where p is a prime number which is a divisor of m, and I a nonzero two-sided ideal of R. Let $D_1$ ; $R\;\times\;R\;\longrightarrow\;and\;$ $D_2\;:\;R\;\times\;R\;longrightarrow\;R$ be symmetric bi-derivations. Suppose further that there exists a symmetric bi-additive mapping B ; $R\;\times\;R\;\longrightarrow\;and\;$ such that $md_1(\chi)\chi ＋ n\chi d_2(\chi)=f(\chi$) holds for all $\chi$$\in$I, where $d_1 \;and\; d_2$ are the traces of $D_1 \;and\; D_2$ respectively and f is the trace of B. Then we have $D_1=0 \;and\; D_2=0$.

• Korean Journal of Mathematics
• /
• v.21 no.2
• /
• pp.161-170
• /
• 2013

Bae and W. Park [3] proved the Hyers-Ulam stability of bi-homomorphisms and bi-derivations in $C^*$-ternary algebras. It is easy to show that the definitions of bi-homomorphisms and bi-derivations, given in [3], are meaningless. So we correct the definitions of bi-homomorphisms and bi-derivations. Under the conditions in the main theorems, we can show that the related mappings must be zero. In this paper, we correct the statements and the proofs of the results, and prove the corrected theorems.

• Communications of the Korean Mathematical Society
• /
• v.15 no.3
• /
• pp.469-479
• /
• 2000

We define and study the extended centroid of a prime $\Gamma$-ring.

• Proceedings of the KIEE Conference
• /
• 1998.07a
• /
• pp.349-352
• /
• 1998

In future superconducting electrical machines and device. AC loss in the superconducting windings are one of the most impotent design paramenters. This paper descriptions a series of Characteristic of a high-Tc superconducting Bi-Pb-Sr-Ca-Cu-O Ag-sheathed filament. In the case simulation and design to reduce ac loss is considered the filament number, twitch pith number and diameter of filament. A filament sample with Tc of 78K is made by $835^{\circ}C$ sintering for 50h and $0.33^{\circ}C$/min heating rate in an atmosphere. The experiment observations are compared with self-field loss and AC losses of Bi-Pb-Sr-Ca-Cu-O filament at 77K in following environments ; (i)AC external parallel magnetic field in different frequencies. And an analytical expression of the loss the derivation of transposition from an optimum condition was derived for the external AC magnetic field, theoretical predictions were found to coincide with the experimental observations.