• Korean Journal of Mathematics
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• 제27권3호
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• pp.779-791
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• 2019

In this paper, we consider derivation of an ordered ${\Gamma}$-semiring and introduce the notion of reverse derivation on ordered ${\Gamma}$-semiring. Also, we obtain some interesting related properties. Let I be a nonzero ideal of prime ordered ${\Gamma}$-semiring M and let d be a nonzero derivation of M. If ${\Gamma}$-semiring M is negatively ordered, then d is nonzero on I.

• 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.

• 대한수학회논문집
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• 제23권4호
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• pp.469-477
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• 2008

We introduce the notion of two-sided $\Gamma$-$\alpha$-derivation of a $\Gamma$-near-ring and give some generalizations of [1, 2].

• Korean Journal of Mathematics
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• 제26권2호
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• pp.175-189
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• 2018

In this paper, at first we generalize the notion of algebra over a field. A ${\Gamma}$-algebra is an algebraic structure consisting of a vector space V, a groupoid ${\Gamma}$ together with a map from $V{\times}{\Gamma}{\times}V$ to V. Then, on every associative ${\Gamma}$-algebra V and for every ${\alpha}{{\in}}{\Gamma}$ we construct an ${\alpha}$-Lie algebra. Also, we discuss some properties about ${\Gamma}$-Lie algebras when V and ${\Gamma}$ are the sets of $m{\times}n$ and $n{\times}m$ matrices over a field F respectively. Finally, we define the notions of ${\alpha}$-derivation, ${\alpha}$-representation, ${\alpha}$-nilpotency and prove Engel theorem in this case.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권4호
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• pp.237-246
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• 2014

Let M be a prime ${\Gamma}$-ring and let d be a derivation of M. If there exists a fixed integer n such that $(d(x){\alpha})^nd(x)=0$ for all $x{\in}M$ and ${\alpha}{\in}{\Gamma}$, then we prove that d(x) = 0 for all $x{\in}M$. This result can be extended to semiprime ${\Gamma}$-rings.

• 대한수학회보
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• 제43권1호
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• pp.9-16
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• 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.

• 대한수학회논문집
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• 제15권3호
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• pp.469-479
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• 2000

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

• Journal of the Optical Society of Korea
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• 제19권3호
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• pp.237-240
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• 2015

We derived the average bit error rate (BER) of coherent free-space optical (FSO) systems with digital binary phase shift keying (BPSK) modulations over atmospheric turbulence channels with a gamma-gamma distribution. To obtain a generalized derivation in a closed-form expression, we used special integrals and transformations of the Meijer G function. Furthermore, we numerically analyzed and simulated the average BER behavior according to the average SNR for different turbulence strengths. Simulation results are demonstrated to confirm the analytical results.

• 충청수학회지
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• 제35권2호
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• pp.115-124
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• 2022

In this paper, we introduce the notion of orthogonal reserve derivation on semiprime 𝚪-semirings. Some characterizations of semiprime 𝚪-semirimgs are obtained by means of orthogonal reverse derivations. We also investigate conditions for two reverse derivations on semiprime 𝚪-semiring to be orthogonal.

• 충청수학회지
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• 제34권2호
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• pp.119-129
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• 2021

In this paper, we introduce the concept of a generalized right f-derivation associated with a derivation d and a function f in 𝚪-incline algebras and give some properties of 𝚪-incline algebras. Also, the concept of d-ideal is introduced in a 𝚪-incline algebra with respect to right f-derivations.