• 대한수학회보
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• 제44권2호
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• pp.241-246
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• 2007

For the evaluation algebra $F[e^{{\pm}x}]_M\;if\;M=\{{\partial}\}$, then $$Der_{non}(F[e^{{\pm}x}]_M)$$ of the evaluation algebra $(F[e^{{\pm}x}]_M)$ is found in the paper [15]. For $M=\{{\partial},\;{\partial}^2\}$, we find $Der_{non}(F[e^{{\pm}x}]_M))$ of the evaluation algebra $F[e^{{\pm}x}]_M$ in this paper. We show that there is a non-associative algebra which is the direct sum of derivation invariant subspaces.

• 대한수학회보
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• 제44권1호
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• pp.95-102
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• 2007

We define the non-associative algebra $\bar{W(n,m,m+s)}$) and we show that it is simple. We find the non-associative algebra automorphism group $Aut_{non}\bar{(W(1,0,0))}\;of\;\bar{W(1,0,0)}$. Also we find that any derivation of $\bar{W(1,0,0)}$ is a scalar derivation in this paper.

• Korean Journal of Mathematics
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• 제30권3호
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• pp.555-560
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• 2022

Suppose L/K be a finite abelian extension of number fields of odd degree and suppose an abelian variety A defined over L is a K-variety. If the endomorphism algebra of A/L is a field F, the followings are equivalent : (1) The enodomorphiam algebra of the restriction of scalars from L to K is simple. (2) There is no proper subfield of L containing L^G_F on which A has a K-variety descent.

• 대한수학회보
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• 제60권4호
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• pp.1025-1034
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• 2023

Let U be the restricted quantized enveloping algebra Ũ_q(𝖘𝖑₂) over an algebraically closed field of characteristic zero, where q is a primitive 𝑙-th root of unity (with 𝑙 being odd and greater than 1). In this paper we show that any indecomposable submodule of U under the adjoint action is generated by finitely many special elements. Using this result we describe all ideals of U. Moreover, we classify annihilator ideals of simple modules of U by generators.

• 충청수학회지
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• 제25권3호
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• pp.445-453
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• 2012

In this paper, we introduce the concept of multiplier in a Hilbert algebra and obtained some properties of multipliers. Also, we introduce the simple multiplier and characterized the kernel of multipliers in Hilbert algebras.

• 대한수학회보
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• 제31권2호
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• pp.167-172
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• 1994

For a given $C^{*}$-dynamical system (A, G, .alpha.) with a G-simple $C^{*}$-algebra A (that is A has no proper .alpha.-invariant ideal) many authors have studied the simplicity of a $C^{*}$-crossed product A $x_{\alpha{r}}$ G. In [1] topological freeness of an action is shown to guarantee the simplicity of the reduced $C^{*}$-crossed product A $x_{\alpha{r}}$ G when A is G-simple. In this paper we investigate the pure infiniteness of a simple $C^{*}$-crossed product A $x_{\alpha}$ G of a purely infinite simple $C^{*}$-algebra A and a topologically free action .alpha. of a finite group G, and find a sufficient condition in terms of the action on the spectrum of the multiplier algebra M(A) of A. Showing this we also prove that some extension of a topologically free action is still topologically free.

• 한국수학사학회지
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• 제13권1호
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• pp.125-136
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• 2000

The notion of MV-algebra was introduced by C.C. Chang in 1958 to provide an algebraic proof of the completeness of Lukasiewicz axioms for infinite valued logic. These algebras appear in the literature under different names: Bricks, Wajsberg algebra, CN-algebra, bounded commutative BCK-algebras, etc. The purpose of this paper is to give a topological lattice completion of semisimple MV-algebras. To this end, we characterize the complete atomic center MV-algebras and semisimple algebras as subalgebras of a cube. Then we define the $\delta$-completion of semisimple MV-algebra and construct the $\delta$-completion. We also study some important properties and extension properties of $\delta$-completion.

• 대한수학회보
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• 제30권2호
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• pp.187-191
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• 1993

In this note we prove the following result: Let A be a complex Banach *-algebra with continuous involution and let B be an $A^{*}$-algebra./T(A) = B. Then T is continuous (Theorem 2). From above theorem some others results of special interest and some well-known results follow. (Corollaries 3,4,5,6 and 7). We close this note with some generalizations and some remarks (Theorems 8.9.10 and question). Throughout this note we consider only complex algebras. Let A and B be complex algebras. A linear mapping T from A into B is called jordan homomorphism if T( $x^{1}$) = (Tx)$^{2}$ for all x in A. A linear mapping T : A .rarw. B is called spectrally-contractive mapping if .rho.(Tx).leq..rho.(x) for all x in A, where .rho.(x) denotes spectral radius of element x. Any homomorphism algebra is a spectrally-contractive mapping. If A and B are *-algebras, then a homomorphism T : A.rarw.B is called *-homomorphism if (Th)$^{*}$=Th for all self-adjoint element h in A. Recall that a Banach *-algebras is a complex Banach algebra with an involution *. An $A^{*}$-algebra A is a Banach *-algebra having anauxiliary norm vertical bar . vertical bar which satisfies $B^{*}$-condition vertical bar $x^{*}$x vertical bar = vertical bar x vertical ba $r^{2}$(x in A). A Banach *-algebra whose norm is an algebra $B^{*}$-norm is called $B^{*}$-algebra. The *-semi-simple Banach *-algebras and the semi-simple hermitian Banach *-algebras are $A^{*}$-algebras. Also, $A^{*}$-algebras include $B^{*}$-algebras ( $C^{*}$-algebras). Recall that a semi-prime algebra is an algebra without nilpotents two-sided ideals non-zero. The class of semi-prime algebras includes the class of semi-prime algebras and the class of prime algebras. For all concepts and basic facts about Banach algebras we refer to [2] and [8].].er to [2] and [8].].

• 대한수학회논문집
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• 제14권1호
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• pp.157-169
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• 1999

We consider the C\ulcorner-algebra O\ulcorner generated by infinite isometries \ulcorner,\ulcorner, …on Hilbert spaces with the property \ulcorner \ulcorner$\leq$1 for every n$\in$N. We present certain type of representations of C\ulcorner-algerbra O\ulcorner on a separable Hilbert space and study the conditions for irreducibility of these representations.

• 충청수학회지
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• 제7권1호
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• pp.75-86
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• 1994

Let L be a Lie algebra over an algebraically closed field F of chracteristic p > 0 which has an $\underline{1}$-filtration. We prove that W(1;$\underline{1}$) is the only restricted simple Lie algebra having an $\underline{1}$-filtration. And we show that the even dimensional Lie algebra can not have an $\underline{1}$-filtration.