• Korean Journal of Mathematics
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• v.28 no.3
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• pp.509-524
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• 2020

The notion of fuzzy closure filters is introduced and discussed in an MS-algebra. In particular, we characterize the prime fuzzy closure filters in terms of boosters. Some relationship between the lattice of fuzzy closure filters and the fuzzy ideal lattice of boosters are explored and investigated.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.907-914
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• 2015

In this paper, we consider a viscoelastic plate equation with p-Laplacian $u^{{\prime}{\prime}}+{\Delta}^2u-div({\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)+{\sigma}(t){\int}_{0}^{t}g(t-s){\Delta}u(s)ds-{\Delta}u^{\prime}=0$. By introducing suitable energy and Lyapunov functionals, we establish a general decay estimate for the energy, which depends on the behavior of both ${\sigma}$ and g.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.917-922
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• 2011

Let R be a prime ring, H a generalized derivation of R, L a noncentral Lie ideal of R, and 0 ${\neq}$ a ${\in}$ R. Suppose that $au^sH(u)u^t$ = 0 for all u ${\in}$ L, where s; t ${\geq}$ 0 are fixed integers. Then H = 0 unless satisfies $S_4$, the standard identity in four variables.

• Bulletin of the Korean Mathematical Society
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• v.46 no.3
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• pp.599-605
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• 2009

Let R be a prime ring, H a generalized derivation of R and L a noncommutative Lie ideal of R. Suppose that $u^sH(u)u^t$ = 0 for all u $\in$ L, where s $\geq$ 0, t $\geq$ 0 are fixed integers. Then H(x) = 0 for all x $\in$ R unless char R = 2 and R satisfies $S_4$, the standard identity in four variables.

• Korean Journal of Mathematics
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• v.7 no.1
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• pp.85-101
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• 1999

Let $p$ be analytic in the unit disc U and let $q$ be univalent in U. In addition, let ${\Omega}$ be a set in C and let ${\psi}:c^3{\times}U{\rightarrow}C$. The author determines conditions on ${\psi}$ so that $$\{{\psi}(p(z),zp^{\prime}(z),z^2p^{{\prime}{\prime}}(z);z){\mid}z{\in}U\}{\subset}{\Omega}{\Rightarrow}p(U){\subset}q(U)$$. Applications of this result to differential inequalities, differential subordinations and integral inequalities are presented.

• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.621-629
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• 2008

Let R be a prime ring of characteristic different from 2, C the extended centroid of R, and $\delta$ a generalized derivations of R. If [[$\delta(x)$, x], $\delta(x)$] = 0 for all $x\;{\in}\;R$ then either R is commutative or $\delta(x)\;=\;ax$ for all $x\;{\in}\;R$ and some $a\;{\in}\;C$. We also obtain some related result in case R is a Banach algebra and $\delta$ is either continuous or spectrally bounded.

• Kyungpook Mathematical Journal
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• v.54 no.1
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• pp.123-129
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• 2014

In this paper the concepts of pure ideals, weakly pure ideals and purely prime ideals in ordered semigroups are introduced. We obtain some characterizations of pure ideals and prove that the set of all pure prime ideals is topologized.

• East Asian mathematical journal
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• v.21 no.1
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• pp.21-26
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• 2005

The purpose of this paper is to show that every generalized Jordan derivation of prime ring with characteristic not two is a generalized derivation on a nonzero Lie ideal U of R such that $u^2{\in}U\;for\;{\forall}u{\in}U$ which is a generalization of the well-known result of I. N. Herstein.

• East Asian mathematical journal
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• v.22 no.2
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• pp.239-248
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• 2006

Let G be a group acting on a ring R. We will define the group action of G on an intuitionsitic fuzzy set of R. We will introduce intuitionistic fuzzy G-prime ideals of a ring and we will prove that every intuitionistic fuzzy G-prime ideal is the largest G-invariant intuitionistic fuzzy ideal of R contained in the intuitionistic fuzzy prime ideal which is uniquely determined up to G-orbits.

• The Pure and Applied Mathematics
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• v.14 no.4
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• pp.271-278
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• 2007

Let R be a 2-torsion free semiprime ring. Suppose that there exists a 4-permuting 4-derivation ${\Delta}:R{\times}R{\times}R{\times}R{\rightarrow}R$ such that the trace is centralizing on R. Then the trace of ${\Delta}$ is commuting on R. In particular, if R is a 3!-torsion free prime ring and ${\Delta}$ is nonzero under the same condition, then R is commutative.