• 대한수학회보
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• 제20권1호
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• pp.31-36
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• 1983

Let R be a commutative ring with 1, and A a unitary commutative R-algebra. By a derivation module of A, we mean a pair (M, d), where M is an A-module and d: A.rarw.M and R-derivation, i.e., d is an R-linear mapping such that d(ab)=a)db)+b(da). A derivation module homomorphism f:(M,d).rarw.(N, .delta.) is an A-homomorphism f:M.rarw.N such that f.d=.delta.. A derivation module of A, (U, d), there exists a unique derivation module homomorphism f:(U, d).rarw.(M,.delta.). In fact, a universal derivation module of A exists in the category of derivation modules of A, and is unique up to unique derivation module isomorphisms [2, pp. 101]. When (U,d) is a universal derivation module of R-algebra A, the A-module U is denoted by U(A/R). For out convenience, U(A/R) will also be called a universal derivation module of A, and d the R-derivation corresponding to U(A/R).

• 대한수학회논문집
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• 제33권1호
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• pp.103-125
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• 2018

Let R be a 5!-torsion free semiprime ring, and let $D:R{\rightarrow}R$ be a Jordan derivation on a semiprime ring R. Then $[D(x),x]D(x)^2=0$ if and only if $D(x)^2[D(x), x]=0$ for every $x{\in}R$. In particular, let A be a Banach algebra with rad(A) and if D is a continuous linear Jordan derivation on A, then we show that $[D(x),x]D(x)2{\in}rad(A)$ if and only if $D(x)^2[D(x),x]{\in}rad(A)$ for all $x{\in}A$ where rad(A) is the Jacobson radical of A.

• 충청수학회지
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• 제13권1호
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• pp.139-144
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• 2000

The generalized noncommutative torus $T_{\rho}^d$ of rank m was defined in [2]. Assume that for the completely irrational noncommutative subtorus $A_{\rho}$ of rank m of $T_{\rho}^d$ there is no integer q > 1 such that $tr(K_0(A_{\rho}))=\frac{1}{q}{\cdot}tr(K_0(A_{\rho^{\prime}}))$ for $A_{\rho^{\prime}}$ a completely irrational noncommutative torus of rank m. All $C^*$-algebras ${\Gamma}({\eta})$ of sections of locally trivial $C^*$-algebra bundles ${\eta}$ over $M=\prod_{i=1}^{e}S^{2k_i}{\times}\prod_{i=1}^{s}S^{2n_i+1}$, $\prod_{i=1}^{s}\mathbb{PR}_{2n_i}$, or $\prod_{i=1}^{s}L_{k_i}(n_i)$ with fibres $T_{\rho}^d{\otimes}M_c(\mathbb{C})$ were constructed in [6, 7, 8]. We prove that ${\Gamma}({\eta}){\otimes}M_{p^{\infty}}$ is isomorphic to $C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C}){\otimes}M_{p^{\infty}}$ if and only if the set of prime factors of cd is a subset of the set of prime factors of p, that $\mathcal{O}_{2u}{\otimes}{\Gamma}({\eta})$ is isomorphic to $\mathcal{O}_{2u}{\otimes}C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C})$ if and only if cd and 2u - 1 are relatively prime, and that $\mathcal{O}_{\infty}{\otimes}{\Gamma}({\eta})$ is not isomorphic to $\mathcal{O}_{\infty}{\otimes}C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C})$ if cd > 1 when no non-trivial matrix algebra can be ${\Gamma}({\eta})$.

• Journal of applied mathematics & informatics
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• 제6권2호
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• pp.611-630
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• 1999

In this paper we show that the Derivation D(A) on the non-commutative Banach algebra A with identity satisfying certain conditions is contained in the radical of A and will show some examples satisfying such properties.

• 대한수학회보
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• 제38권3호
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• pp.443-447
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• 2001

The main goal of this paper is to show the following: Let d and g be (continuous or discontinuous) linear derivations on a Banach algebra A over a complex field C such that $\alphad^3+dg$ is a linear Jordan derivation for some $\alpha\inC$. Then the product dg maps A into the Jacobson radical of A.

• 호남수학학술지
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• 제35권2호
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• pp.201-210
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• 2013

In this paper, we introduced the notion of multiplier of a BCC-algebra, and gave some properties of BCC-algebras. Also, we characterized kernels and normal ideals of multipliers on BCC-algebras.

• 충청수학회지
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• 제30권4호
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• pp.357-367
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• 2017

In this paper, we introduce the notion of multiplier of AC-algebra and consider the properties of multipliers in AC-algebras. Also, we characterized the fixed set $Fix_d(X)$ by multipliers. Moreover, we prove that M(X), the collection of all multipliers of AC-algebras, form a semigroup under certain binary operation.

• 대한수학회보
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• 제37권4호
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• pp.779-790
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• 2000

Let $D_3$ be the Dickson invariant algebra of $F_2[X_1,\; X_2,\; X_3] \; by \; GL(3,\; F_2)$. In this paper, we provide an elementary proof of Theorem 3.2 of [2]; each element in $D_3$ is hit by the Steenrod square in $F_2[X_1,\; X_2,\; X_3]$.

• 호남수학학술지
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• 제36권4호
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• pp.885-893
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• 2014

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

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제12권1호
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• pp.65-73
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• 2005

Let g = g(A) = (equation omitted) + be a symmetrizable Kac-Moody Lie algebra of type D/sub l//sup (1) with W as its Weyl group. We construct a sequence of root spaces with certain conditions. We also find the number of terms of this sequence is less then or equal to the hight of θ, the highest root.