• 충청수학회지
• /
• 제12권1호
• /
• pp.15-21
• /
• 1999

In this paper, we introduce the notion of anti fuzzy prime ideals in a commutative BCK-algebra and obtain some properties of it.

• East Asian mathematical journal
• /
• 제21권2호
• /
• pp.171-181
• /
• 2005

In this paper we investigate some more properties of of $S_3$-algebras. We also prove that the class of $S_3$-algebras is contained in the class of commutative BCI-algebras.

• 대한수학회보
• /
• 제36권3호
• /
• pp.503-512
• /
• 1999

Over a field k, every schur k-algebra is a cyclotomic algebra due to Brauer-Witt theorem. Similarly every projective Schur k-division algebra is itself a radical algebra by Aljadeff-Sonn theorem. We study the two theorems over a certain commutative ring, and prove similar results over regular domain containing a field.

• 한국수학사학회지
• /
• 제20권1호
• /
• pp.73-82
• /
• 2007

본 논문은 Wajsberg hoops, BCK-대수와 MV-대수의 도입과 그 발전과정을 간단히 소개하고, Wajsberg hoops, MV-대수, 그리고 가환 BCK-대수의 관계를 살펴본다. 특히 모든 Wajsberg 대수는 가환 BCK-대수가 됨을 규명한다.

• Kyungpook Mathematical Journal
• /
• 제50권1호
• /
• pp.81-87
• /
• 2010

We modify the definition of difference algebra given by J. Meng to obtain a structure which is a directoid with sectional switching involutions with respect to the given partial order. Moreover, we show that this is a representation of our skew difference algebras because every such directoid can be converted into a skew difference algebra.

• 호남수학학술지
• /
• 제26권4호
• /
• pp.483-507
• /
• 2004

In this paper the left regular representation and the reduced $C^*$-algebra for a commutative separative semigroup is defined. The universal representation, the reduced $C^*$-algebra and the full $C^*$-algebra for the additive semigroup $N^+$ are given. Also it is proved that $C*_r(N^+){\ncong}C^*(N^+)$.

• 호남수학학술지
• /
• 제26권4호
• /
• pp.471-481
• /
• 2004

In this paper we introduce the notion of a (pre-)Coxeter algebra and show that a Coxeter algebra is equivalent to an abelian group all of whose elements have order 2, i.e., a Boolean group. Moreover, we prove that the class of Coxeter algebras and the class of B-algebras of odd order are Smarandache disjoint. Finally, we show that the class of pre-Coxeter algebras and the class of BCK-algebras are Smarandache disjoint.

• 한국수학사학회지
• /
• 제13권1호
• /
• pp.125-136
• /
• 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
• /
• 제32권2호
• /
• pp.367-372
• /
• 1995

In 1955 Singer and Wermer [12] proved that every bounded derivation on a commutative Banach algebra maps into its radical. They conjectured that the continuity of the derivation in their theorm can be removed. In 1988 Thomas [13] proved their conjecture ; Every derivation on a commutative Banach algebra maps into its radical. For noncommutative versions, in 1984 B. Yood [15] proved that the continuous derivations on Banach algebras satisfing [D(a),b] $\in$ Rad(A) for all a, b $\in$ A have the radical range, where [a,b] will be denote the commutator ab-ba. In 1990 M.Bresar and J.Vukman [1] have generlized Yood's result, that is, the continuous linear Jordan derivation on Banach algebra that satisfies [D(a),a] $\in$ Rad(A) for all a $\in$ A has the radical range. In next year Mathieu and Murphy [5] proved that every bounded centralizing derivation on Banach algebras has its image in the radical. Mathieu and Runde [6] removed the boundedness of that.

• 호남수학학술지
• /
• 제27권3호
• /
• pp.399-404
• /
• 2005

Let M be a finite commutative nilpotent algebra over a perfect field k of prime characteristic p and let $M^p$ be the sub-algebra of M generated by $x^p$, $x{\in}M$. Eggert[3] conjectures that $dim_kM{\geq}pdim_kM^p$. In this paper, we show that the conjecture holds for $M=R^+/I$, where $R=k[X_1,\;X_2,\;{\cdots},\;X_t]$ is a polynomial ring with indeterminates $X_1,\;X_2,\;{\cdots},\;X_t$ over k and $R^+$ is the maximal ideal of R generated by $X_1,\;X_2,{\cdots},\;X_t$ and I is a monomial ideal of R containing $X_1^{n_1+1},\;X_2^{n_2+1},\;{\cdots},\;X_t^{n_t+1}$ ($n_i{\geq}0$ for all i).