• Journal of the Chungcheong Mathematical Society
• /
• v.15 no.1
• /
• pp.25-33
• /
• 2002

We prove the generalized Hyers-Ulam-Rassias stability of linear operators in a Hilbert module over a unital $C^*$-algebra.

• Journal of the Chungcheong Mathematical Society
• /
• v.12 no.1
• /
• pp.187-191
• /
• 1999

In this paper we will show that if [G(y), x]D(x) lies in the nil radical of A for all $x{\in}A$, then GD maps A into the radical, where D and G are derivations on a Banach algebra A.

• Journal for History of Mathematics
• /
• v.12 no.1
• /
• pp.21-31
• /
• 1999

This paper deals with the development of universal algebras. We first investigate how the abstract algebra has emerged as a common generalization of arithmetic and algebra of logic, which was finalized by A. N. Whitehead in his "A treatise on universal algebra with applications." And we investigate also the process of formalizing universal algebras by G. Birkhoff. Birkhoff.

• Bulletin of the Korean Mathematical Society
• /
• v.42 no.2
• /
• pp.379-386
• /
• 2005

In this paper, we consider a collection of ideals of a difference algebra X. We use the concept of congruence relation with respect to ideals to construct a uniformity that induces a topology on X which makes this to a topological difference algebras. We study the properties of this topology regarding different ideals.

• East Asian mathematical journal
• /
• v.26 no.3
• /
• pp.379-387
• /
• 2010

In this paper, we prove that the extension ideal of a fuzzy characteristic ideal of a positive implicative BCK-algebra is a fuzzy characteristic ideal. We introduce the notion of the extension of intuitionistic fuzzy ideal of BCK-algebras and some properties of fuzzy intuitionistic ideal extensions of BCK-algebra are investigated.

• Communications of the Korean Mathematical Society
• /
• v.18 no.2
• /
• pp.225-233
• /
• 2003

In this paper, we obtain Hon(P,- ) is an exact functor if P is a p-projective BCI-algebra.

• Bulletin of the Korean Mathematical Society
• /
• v.37 no.2
• /
• pp.265-272
• /
• 2000

Let D be a derivation on an Banach algebra A. Suppose that [[D(x), x], D(x)] lies in the nil radical of A for all $x{\;}{\in}{\;}A$. Then D(A) is contained in the Jacobson radical of A.

• Korean Journal of Mathematics
• /
• v.22 no.4
• /
• pp.659-670
• /
• 2014

In this paper, we prove the Hyers-Ulam stability of homomorphisms in fuzzy Banach algebras and of derivations on fuzzy Banach algebras associated to the Cauchy-Jensen functional equation.

• Journal of the Chungcheong Mathematical Society
• /
• v.27 no.4
• /
• pp.643-649
• /
• 2014

In this paper, we introduce the concept of a (f, g)-derivation which is a generalization of f-derivation in an incline algebra and give some properties of incline algebras. Also, we consider the kerd and k-ideal with respect to (f, g)-derivation in an incline algebra.

• Journal of the Chungcheong Mathematical Society
• /
• v.7 no.1
• /
• pp.75-86
• /
• 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.