• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.319-327
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• 2000

In this paper we investigate the conditions for derivations under which the Singer-Wermer theorem is true for noncommutative Banach algebra A such that either [[D(x),xD(x)] ${\in}$ rad(A) for all $x{\in}$A or $D(x)^2$x+xD(x))$^2$${\in}$rad(A) for all $x{\in}$A, where rad(A) is the Jacobson radical of A, then $D(A){\subseteq}$rad(A).

• Bulletin of the Korean Mathematical Society
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• v.26 no.1
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• pp.31-34
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• 1989

In this paper we show that if there is a derivation on a commutative Banach algebra which has a non-nilpotent separating space, then there is a discontinuous derivation on a commutative Banach algebra which has a range in its radical. Also we show that if every prime ideal is closed in a commutative Banach algebra with identity then every derivation on it has a range in its radical.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1387-1408
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• 2022

Let R be a commutative ring with a non-zero identity, S be a multiplicatively closed subset of R and M be a unital R-module. In this paper, we define a submodule N of M with (N :_R M)∩S = ∅ to be weakly S-prime if there exists s ∈ S such that whenever a ∈ R and m ∈ M with 0 ≠ am ∈ N, then either sa ∈ (N :_R M) or sm ∈ N. Many properties, examples and characterizations of weakly S-prime submodules are introduced, especially in multiplication modules. Moreover, we investigate the behavior of this structure under module homomorphisms, localizations, quotient modules, cartesian product and idealizations. Finally, we define two kinds of submodules of the amalgamation module along an ideal and investigate conditions under which they are weakly S-prime.

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.127-139
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• 1997

The spherical non-commutative $\mathbb{S}_{\omega}$ were defined in [2,3]. Assume that no non-trivial matrix algebra can be factored out of the $\mathbb{S}_{\omega}$, and that the fibres are isomorphic to the tensor product of a completely irrational non-commutative torus with a matrix algebra $M_k(\mathbb{C})$. It is shown that the tensor product of the spherical non-commutative torus $\mathbb{S}_{\omega}$ with the even Cuntz algebra $\mathcal{O}_{2d}$ has a trivial bundle structure if and only if k and 2d - 1 are relatively prime, and that the tensor product of the spherical non-commutative torus $S_{\omega}$ with the generalized Cuntz algebra $\mathcal{O}_{\infty}$ has a non-trivial bundle structure when k > 1.

• Honam Mathematical Journal
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• v.16 no.1
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• pp.63-66
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• 1994

• 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.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.

• Communications of the Korean Mathematical Society
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• v.36 no.4
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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.

• Korean Journal of Mathematics
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• v.31 no.3
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• pp.313-321
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• 2023

In this paper, we explore the additivity of the map Ω : 𝒜 → 𝒜 that satisfies Ω([ℒ, ℳ]_*)=[Ω (ℳ), ℒ]_* + [ℳ, Ω(ℒ)]_*, where [ℒ, ℳ]_*= ℒℳ^* - ℳ ℒ^*, for all ℒ, ℳ ∈ 𝒜, a prime *-algebra with unit ℐ. Additionally we show that if Ω (αℐ) is self-adjoint operator for α ∈ {1, i} then Ω = 0.

• Journal of the Korean Mathematical Society
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• v.50 no.3
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• pp.591-605
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• 2013

The underlying field is of characteristic $p$ > 2. In this paper, we first use the method of computing the homogeneous derivations to determine the first cohomology of the so-called odd contact Lie algebra with coefficients in the even part of the generalized Witt Lie superalgebra. In particular, we give a generating set for the Lie algebra under consideration. Finally, as an application, the derivation algebra and outer derivation algebra of the Lie algebra are completely determined.