• 대한수학회지
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• 제36권3호
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• pp.593-607
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• 1999

Let denote the orthosymplectic Lie superalgebra spo (2m,1). For each irreducible -module, we describe its character in terms of tableaux. Using this result, we decompose kV, the k-fold tensor product of the natural representation V of , into its irreducible -submodules, and prove that the Brauer algebra Bk(1-2m) is isomorphic to the centralizer algebra of spo(2m, 1) on kV for m .

• Kyungpook Mathematical Journal
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• 제58권3호
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• pp.481-488
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• 2018

Let I be a ${\ast}$-ideal on a 2-torsion free ${\ast}$-prime ring and $F:R{\rightarrow}R$ a generalized derivation with an associated derivation $d:R{\rightarrow}R$. The aim of this paper is to explore the condition under which generalized derivation F becomes a left centralizer i.e., associated derivation d becomes a trivial map (i.e., zero map) on R.

• 대한수학회논문집
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• 제4권1호
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• pp.83-87
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• 1989

• 한국수학교육학회지시리즈A:수학교육
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• 제13권3호
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• pp.11-15
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• 1975

• 대한수학회지
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• 제47권3호
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• pp.523-535
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• 2010

In this paper, we show that Jordan $\tau$-centralizers and local $\tau$-centralizers are $\tau$-centralizers under certain conditions. We also discuss a new type of generalized derivations associated with Hochschild 2-cocycles and introduce a special local generalized derivation associated with Hochschild 2-cocycles. We prove that if $\cal{L}$ is a CDCSL and $\cal{M}$ is a dual normal unital Banach $alg\cal{L}$-bimodule, then every local generalized derivation of above type from $alg\cal{L}$ into $\cal{M}$ is a generalized derivation.

• Korean Journal of Mathematics
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• 제27권4호
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• pp.977-1003
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• 2019

Let 𝓐 and 𝓑 be two unital C^⁎-algebras and 𝓐 ⊗ 𝓑 be their algebraic tensor product. For two bilinear maps on 𝓐 and 𝓑 with some specific conditions, we derive a bilinear map on 𝓐 ⊗ 𝓑 and study some characteristics. Considering two 𝓐 ⊗ 𝓑 bimodules, a centralizer is also obtained for 𝓐 ⊗ 𝓑 corresponding to the given bilinear maps on 𝓐 and 𝓑. A relationship between orthogonal complements of subspaces of 𝓐 and 𝓑 and their tensor product is also deduced with suitable example.

• 대한수학회논문집
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• 제27권1호
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• pp.69-76
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• 2012

Let R be a ring, and ${\alpha}$ be an endomorphism of R. An additive mapping H : R ${\rightarrow}$ R is called a left ${\alpha}$-multiplier (centralizer) if H(xy) = H(x)${\alpha}$(y) holds for all x,y $\in$ R. In this paper, we shall investigate the commutativity of prime and semiprime rings admitting left ${\alpha}$-multiplier satisfying any one of the properties: (i) H([x,y])-[x,y] = 0, (ii) H([x,y])+[x,y] = 0, (iii) $H(x{\circ}y)-x{\circ}y=0$, (iv) $H(x{\circ}y)+x{\circ}y=0$, (v) H(xy) = xy, (vi) H(xy) = yx, (vii) $H(x^2)=x^2$, (viii) $H(x^2)=-x^2$ for all x, y in some appropriate subset of R.

• 대한수학회논문집
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• 제36권2호
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• pp.229-238
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• 2021

Let R be a ring with characteristic different from 2. An additive mapping F : R → R is called a generalized derivation on R if there exists a derivation d : R → R such that F(xy) = F(x)y + xd(y) holds for all x, y ∈ R. In the present paper, we show that if R is a prime ring satisfying certain identities involving a generalized derivation F associated with a derivation d, then R becomes commutative and in some cases d comes out to be zero (i.e., F becomes a left centralizer). We provide some counter examples to justify that the restrictions imposed in the hypotheses of our theorems are not superfluous.

• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.709-717
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• 2022

The objective of this research is to prove that an additive mapping T : R → R is a left as well as right centralizer on R if it satisfies any one of the following identities: (i) T(xⁿyⁿ + yⁿxⁿ) = T(xⁿ)yⁿ + yⁿT(xⁿ) (ii) 2T(xⁿyⁿ) = T(xⁿ)yⁿ + yⁿT(xⁿ) for each x, y ∈ R, where n ≥ 1 is a fixed integer and R is any n!-torsion free semiprime ring. In addition, we talk over above identities in the setting of *-ring(ring with involution).

• Korean Journal of Mathematics
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• 제17권4호
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• pp.437-449
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• 2009

In this paper, we establish the stability of cubic double centralizers and cubic multipliers on Banach algebras. We also prove the superstability of cubic double centralizers on Banach algebras which are cubic commutative and cubic without order.