• 호남수학학술지
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• 제27권1호
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• pp.77-82
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• 2005

$C^*$-algebras which are closed sub-algebras of Banach algebras have been studied many years ago. In this note we extend the main definition of $C^*$-algebras to metrizable topological algebras.

• 호남수학학술지
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• 제23권1호
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• pp.59-66
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• 2001

A class of topological algebras, which we call it a fundamental one, has already been introduced to generalize the locally bounded and locally convex algebras. To prove the basic theorems on fundamental algebras, the first successful step is the new version of the Cohen factorization theorem. Here we recall it and prove some new results on fundamental topological algebras.

• 호남수학학술지
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• 제26권1호
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• pp.77-83
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• 2004

A class of topological algebras, which we call it a fundamental one, has already been introduced generalizing the famous Cohen factorization theorem to more general topological algebras. To prove the generalized versions of Cohen's theorem to locally multilplicatively convex algebras, and finally to fundamental topological algebras, the completness of the background spaces is one of the main conditions. The local convexity of the completion of a locally convex space is a well known fact and here we have a discussion on the completness of fundamental metrizable topological vector spaces.

• 호남수학학술지
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• 제30권2호
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• pp.247-258
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• 2008

In this paper, we show how certain topologies associate with ideals of subtraction algebras on subtraction algebras. We show subtraction algebras to be topological subtraction algebras with respect to theses topologies. Furthermore, we show how certain standard properties may arise. In addition we demonstrate that it is natural for these topologies to have many clop en sets and thus to be highly disconnected via the ideal theory of subtraction algebras.

• 대한수학회논문집
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• 제23권2호
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• pp.169-178
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• 2008

In this paper, we show how to associate certain topologies with special ideals of BCC-algebras on these BCC-algebras. We show that it is natural for BCC-algebras to be topological BCC-algebras with respect to theses topologies. Furthermore, we show how certain standard properties may arise. In addition we demonstrate that it is natural for these topologies to have many clopen sets and thus to be highly connected via the ideal theory of BCC-algebras.

• 대한수학회보
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• 제36권1호
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• pp.109-117
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• 1999

We introduce the notion of a fuzzy topological implicative algebras and apply some of Foster's results [2] to homomorphic images and inverse images of fuzzy topological implicative algebras.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권3호
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• pp.237-248
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• 2023

The aim of this paper is to study the concept of s-topological d-algebras which is a d-algebra supplied with a certain type of topology that makes the binary operation defined on it d-topologically continuous. This concept is a generalization of the concept of topological d-algebra. We obtain several properties of s-topological d-algebras.

• 대한수학회논문집
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• 제25권3호
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• pp.335-342
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• 2010

The structure of fuzzy topological spaces based on WFI-algebras is considered. The notions of WFI-fuzzy topological spaces and WFI-fuzzy continuous mappings are introduced, and several properties are investigated. A relation between WFI-homomorphism and WFI-fuzzy continuous mapping is given.

• 호남수학학술지
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• 제42권3호
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• pp.501-510
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• 2020

This paper considers coupled fixed point theorems on unital without of order semi-simple fundamental locally multiplicative topological algebras (abbreviated by FLM algebras).

• 대한수학회보
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• 제42권2호
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• pp.379-386
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• 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.