• Journal for History of Mathematics
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• v.13 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.299-302
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• 1994

Throughout this paper, let X be a compact Hausdorff space, and let C(X) (resp. $C_{R}$ /(X)) be the complex (resp. real) Banach algebra of all continuous complex-valued (resp. real-valued) functions on X with the pointwise operations and the supremum norm x. A Banach function algebra on X is a Banach algebra lying in C(X) which separates the points of X and contains the constants. A Banach function algebra on X equipped with the supremum norm is called a uniform algebra on X, that is, a uniformly closed subalgebra of C(X) which separates the points of X and contains the constants.(omitted)

• Journal of the Korean Mathematical Society
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• v.40 no.2
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• pp.273-286
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• 2003

Let $F^{\alpha}$G be a twisted group algebra. A subalgebra of $F^{\alpha}$G generated by all class sums of partition P of G is called a projective class algebra in $F^{alpha}$G associated with partition P. In this paper we study various partitions of G determined by actions of certain operator groups on G and construct projective class algebras depending on the actions. With regard to projective class algebras, we investigate structures of associated skew group algebras and fixed group algebras.

• The Pure and Applied Mathematics
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• v.19 no.3
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• pp.297-304
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• 2012

There are several types of orders in a Quaternion algebra. Generally, zeta functions defined on orders of a Quaternion algebra give some informations on the ideal theory of orders. In this study, we investigate functional equalities between the zeta functions defined on orders of a Quaternion algebra.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.95-106
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• 2016

As a generalization of Q-algebra, the notion of pseudo Q-algebra is introduced, and some of their properties are investigated. The notions of pseudo subalgebra, pseudo ideal, and pseudo atom in a pseudo Q-algebra are introduced. Characterizations of their properties are provided.

• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.125-134
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• 1993

Let X be a compact Hausdorff space, and let C(X) (resp. $C_{R}$(X)) be the complex (resp. real) Banach algebra of all continuous complex-valued(resp. real-valued) functions on X with the pointwise operations and the supremum norm x. A Banach function algebra on X is a Banach algebra lying in C(X) which separates the points of X and contains the constants. A Banach function algebra on X equipped with the supremum norm is called a uniform algebra on X, that is, a uniformly closed subalgebra of C(X) which separates the points of X and contains the constants.s.

• Communications of the Korean Mathematical Society
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• v.25 no.3
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• pp.365-372
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• 2010

In this paper, we show that the mapping ${\varphi}(x)\;=\;0*x$ is an endomorphism of a Q-algebra X, which induces a congruence relation "~" such that X/$\varphi$ is a medial Q-algebra. We also study some decompositions of ideals in Q-algebras and obtain equivalent conditions for closed ideals. Moreover, we show that if I is an ideal of a Q-algebra X, then $I^g$ is an ignorable ideal of X.

• Bulletin of the Korean Mathematical Society
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• v.58 no.5
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• pp.1193-1208
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• 2021

Let 𝓐 be a von Neumann algebra with no central summands of type I₁. In this article, we study Lie n-derivation on von Neumann algebra and prove that every additive Lie n-derivation on a von Neumann algebra has standard form at zero product as well as at projection product.

• Korean Journal of Mathematics
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• v.29 no.3
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• pp.563-576
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• 2021

In this paper, we introduce the notion of intuitionistic fuzzy PMS-subalgebra of a PMS-algebra. The idea of level subsets of an intuitionistic fuzzy PMS-subalgebra of a PMS-algebra is introduced. The relation between intuitionistic fuzzy sets and their level sets in a PMS-algebra is examined, and some interesting results are obtained.

• Korean Journal of Mathematics
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• v.29 no.3
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• pp.621-629
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• 2021

The idea of C^*-algebra valued metric spaces was given by Ma, Jiang and Sun. In this paper we have studied the ideas of I-Cauchy and I^*-Cauchy sequences and their properties in such spaces and also we give the idea of C^*-algebra valued normed spaces.