• Bulletin of the Korean Mathematical Society
• /
• v.39 no.2
• /
• pp.259-267
• /
• 2002

Let X be a hemicompact space with ($K_{n}$) as an admissible exhaustion, and for each n $\in$ N, $A_{n}$ a Banach function algebra on $K_{n}$ with respect to $\parallel.\parallel_n$ such that $A_{n+1}\midK_{n}$$\subsetA_n$ and${\parallel}f{\mid}K_n{\parallel}_n{\leq}{\parallel}f{\parallel}_{n+1}$ for all f$\in$$A_{n+1}$, We consider the subalgebra A = { f $\in$ C(X) : $\forall_n\;{\epsilon}\;\mathbb{N}$ of C(X) as a frechet function algebra and give a result related to its spectrum when each $A_{n}$ is natural. We also show that if X is moreover noncompact, then any closed subalgebra of A cannot be topologized as a regular Frechet Q-algebra. As an application, the Lipschitzalgebra of infinitely differentiable functions is considered.d.

• Bulletin of the Korean Mathematical Society
• /
• v.39 no.3
• /
• pp.471-478
• /
• 2002

Let $Let\eta={\eta m}m$ be an eventually constant sequence of unit vectors $\eta m$ in $C^{n}$ and let $\rho$η be the pure state on $UHF_{n}$ algebra which is defined by $\rho\eta(\upsilon_i_1....\upsilon_i_k{\upsilon_{j1}}^*...{\upsilon_{j1}}^*)={\eta_1}^{i1}...{\eta_k}^{ik}{\eta_k}^{jk}...{\eta_1}^{j1}$. We find infinitely many state extensions of $\rho\eta$ to Cuntz algebra $O_n$ using representations and unitary operators. Also, we present theirconcrete expressions.

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.4
• /
• pp.703-706
• /
• 2013

Let R be a commutative noetherian algebra and let ${\delta}$ be a nonzero derivation. Here we determine the prime ideals of the skew polynomial algebra R[z;${\delta}$] and the Poisson prime ideals of R[z;${\delta}$]p.

• The Pure and Applied Mathematics
• /
• v.15 no.3
• /
• pp.309-313
• /
• 2008

The notion of central Hilbert algebras and central deductive systems is introduced, and related properties are investigated. We show that the central part of a Hilbert algebra is a deductive system. Conditions for a subset of a Hilbert algebra to be a deductive system are given. Conditions for a subalgebra of a Hilbert algebra to be a deductive system are provided.

• Journal of Educational Research in Mathematics
• /
• v.17 no.3
• /
• pp.253-270
• /
• 2007

by A.C. Clairaut was written based on the historico-genetic principle such as his . In this paper, by analyzing his we can induce six principles that Clairaut adopted to teach algebra: necessity and curiosity as a motive of studying algebra, harmony of discovery and proof, complementarity of generalization and specialization, connection of knowledge to be learned with already known facts, semantic approaches to procedural knowledge of mathematics, reversible approach. These can be considered as strategies for teaching algebra accorded with beginner's mind. Some of them correspond with characteristics of , but the others are unique in the domain of algebra. And by comparing Clairaut's approaches with school algebra, we discuss about some mathematical subjects: setting equations in relation to problem situations, operations and signs of letters, rule of signs in multiplication, solving quadratic equations, and general relationship between roots and coefficients of equations.

• Bulletin of the Korean Mathematical Society
• /
• v.38 no.4
• /
• pp.803-814
• /
• 2001

A projective Schur algebra associated with a partition of finite group G can be constructed explicitly by defining linear transformations of G. We will consider various linear transformations and count the number of equivalent classes in a finite group. Then we construct projective Schur algebra dimension is determined by the number of classes.

• Honam Mathematical Journal
• /
• v.28 no.4
• /
• pp.559-572
• /
• 2006

The notion of simulative and mutant WFI-algebras is introduced, and several properties are investigated. Characterizations of a simulative WFI-algebra are established. A relation between an associative WFI-algebra and a simulative WFI-algebra is given. Some types for a simulative WFI-algebra to be mutant are found.

• Journal of the Chungcheong Mathematical Society
• /
• v.27 no.1
• /
• pp.57-64
• /
• 2014

It is known that the class of CI-algebras is a generalization of the class of BE-algebras [5]. Recently, K. H. Kim introduced the notion of a CS-algebra [4]. In this paper we discuss a closed deductive system of a CS-algebra, and we find some fundamental properties. Moreover, we study a CS-algebra homomorphism and a congruence relation.

• Kyungpook Mathematical Journal
• /
• v.50 no.1
• /
• 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.

• Journal of applied mathematics & informatics
• /
• v.20 no.1_2
• /
• pp.569-573
• /
• 2006

Nagata and Higman proved that any nil-algebra of finite nilindex is nilpotent of finite index. The Nagata-Higman Theorem can be formulated in terms of T-ideals. TheT-ideal generated by $a^n$ for all $a{\in}A$ is also generated by the symmetric polynomials. The symmetric polynomials play an importmant role in analyzing nil-algebra. We construct the incidence matrix with the symmetric polynomials. Using this incidence matrix, we determine the nilpotency index of nil-algebra of nil-index 3.