• 대한수학회보
• /
• 제41권2호
• /
• pp.359-369
• /
• 2004

The purpose of this paper is to compare the radicals of a left symmetric algebra considered in 〔1〕 when the associated Lie algebra is nilpotent. In this case, we show that all the radicals considered there are equal. We also consider some other radicals and show they are also equal.

• 대한수학회논문집
• /
• 제17권2호
• /
• pp.237-243
• /
• 2002

In this paper we generalize the Lie algebras of KPS's in [4], which have no toral elements. However our generalized Lie algebras have toral elements. Moreover our Lie algebras are not isomorphic to the Witt algebra W(n) with a toral element.

• 대한수학회논문집
• /
• 제11권3호
• /
• pp.595-600
• /
• 1996

We give a characterization of a deductive system. We introduce the concept of maximal deductive systems and show that every bounded Hilbert algebra with at least two elements contains at least one maximal deductive system. Moreover, we introduce the notion of radical and semisimple in a Hilbert algebra and prove that if H is a bounded Hilbert algebra in which every element is an involution, then H is semisimple.

• Korean Journal of Mathematics
• /
• 제26권1호
• /
• pp.53-60
• /
• 2018

In this paper, we consider the question of the Rota-Baxter operators of 3-dimensional Heisenberg Lie algebra on ${\mathbb{F}}$, where ${\mathbb{F}}$ is an algebraic closed field. By using the Lie product of the basis elements of Heisenberg Lie algebras, all Rota-Baxter operators of 3-dimensional Heisenberg Lie algebras are calculated and left symmetric algebras of 3-dimensional Heisenberg Lie algebra are determined by using the Yang-Baxter operators.

• Korean Journal of Mathematics
• /
• 제28권1호
• /
• pp.17-30
• /
• 2020

In this paper, we firstly introduce the class of C^*-algebra valued symmetric spaces and utilize the same to prove our fixed point results. We furnish an example to highlight the utility of our main result. Finally, we apply our result to examine the existence and uniqueness of a solution for a system of Fredholm integral equations.

• 호남수학학술지
• /
• 제7권1호
• /
• pp.119-127
• /
• 1985

A study is made of a special type of $C^{\ast}$ -dynamical systems, consisting of a class $n^{\infty}$ uniformly hyperfinite $C^{\ast}$-algebra A, the torus group $G=T^{d}$ ($$1{\leq_-}d{\leq_-}n-1$$) and a natural product action of G on A by $^{*}-automorphisms$. We give some conditions for product states on the fixed point algebra $A^{G}$ of A by G to be factorial.

• 충청수학회지
• /
• 제15권1호
• /
• pp.53-60
• /
• 2002

In this paper, we prove the generalized Hyers-Ulam-Rassias stability of linear operators in Banach modules over a unital $C^*$-algebra associated with its unitary group.

• 충청수학회지
• /
• 제22권2호
• /
• pp.123-129
• /
• 2009

We introduce the notion of Smarandache GT-algebras, and the notion of Smarandache GT-filters of the Smarandache GT- algebra related to the Tarski algebra, and related some properties are investigated.

• 대한수학회보
• /
• 제40권1호
• /
• pp.53-61
• /
• 2003

We prove the generalized Hyers-Ulam-Rassias stability of the invertible mapping in a Banach module over a unital Banach algebra, and prove the generalized Hyers-Ulam-Rassias stability of the Jensen's functional equations in a Hilbert module over a unital $C^{*}$-algebra.

• 대한수학회지
• /
• 제43권1호
• /
• pp.77-86
• /
• 2006

We consider the set of commuting pairs of matrices and their preservers over binary Boolean algebra, chain semiring and general Boolean algebra. We characterize those linear operators that preserve the set of commuting pairs of matrices over a general Boolean algebra and a chain semiring.