• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.217-222
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• 2012

In this note we investigate some properties of ${\beta}$-algebras and further relations with $B$-algebras. Especially, we show that if ($X$, -, +, 0) is a $B^*$-algebra, then ($X$, +) is a semigroup with identity 0. We discuss some constructions of linear ${\beta}$-algebras in a field $K$.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.939-959
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• 2019

Using generalized graded crossed products, we give necessary and sufficient conditions for a simple algebra over a Henselian valued field (under some hypotheses) to have Kummer subfields. This study generalizes some known works. We also study many properties of generalized graded crossed products and conditions for embedding a graded simple algebra into a matrix algebra of a graded division ring.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.445-463
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• 2019

Let C[0, T] denote the space of continuous real-valued functions on [0, T]. On the space C[0, T], we introduce a Banach algebra of series of functions which are generalized Fourier-Stieltjes transforms of measures of finite variation on the product of simplex and Euclidean space. We evaluate analytic Feynman integrals of the functions in the Banach algebra which play significant roles in the Feynman integration theory and quantum mechanics.

• Honam Mathematical Journal
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• v.41 no.2
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• pp.435-447
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• 2019

The notions of a neutrosophic subalgebra and a neutrosohic ideal of a subtraction algebra are introduced. Characterizations of a neutrosophic subalgebra and a neutrosophic ideal are investigated. We show that the homomorphic preimage of a neutrosophic subalgebra of a subtraction algebra is a neutrosophic subalgebra, and the onto homomorphic image of a neutrosophic subalgebra of a subtraction algebra is a neutrosophic subalgebra.

• Korean Journal of Mathematics
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• v.29 no.2
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• pp.271-291
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• 2021

Hom-Lie-Yamaguti color algebras are defined and their representation and cohomology theory is considered. The (2, 3)-cocycles of a given Hom-Lie-Yamaguti color algebra T are shown to be very useful in a study of its deformations. In particular, it is shown that any (2, 3)-cocycle of T gives rise to a Hom-Lie-Yamaguti color structure on T⊕V , where V is a T-module, and that a one-parameter infinitesimal deformation of T is equivalent to that a (2, 3)-cocycle of T (with coefficients in the adjoint representation) defines a Hom-Lie-Yamaguti color algebra of deformation type.

• Honam Mathematical Journal
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• v.43 no.2
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• pp.325-342
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• 2021

In this paper, we define a new algebraic structure known as a generalized pseudo BE-algebra which is a generalization of a pseudo BE-algebra. We construct some examples in order to show the existence of the generalized pseudo BE-algebra. Moreover, we characterize different classes of generalized pseudo BE-algebras by some results.

• The Pure and Applied Mathematics
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• v.30 no.3
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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.

• The Pure and Applied Mathematics
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• v.30 no.1
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• pp.15-24
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• 2023

In this paper, we show that bounded Hochschild homology and cohomology of associated matrix Banach algebra 𝔊(𝔄, R, S, 𝔅) to a Morita context 𝔐(𝔄, R, S, 𝔅, { }, [ ]) are isomorphic to those of the Banach algebra 𝔄. Consequently, we indicate that the n-amenability and simplicial triviality of 𝔊(𝔄, R, S, 𝔅) are equivalent to the n-amenability and simplicial triviality of 𝔄.

• The Pure and Applied Mathematics
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• v.30 no.4
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• pp.407-416
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• 2023

In this paper, we introduce the concept of C^*-algebra-valued quasi b-metric space and prove some existence and uniqueness theorems. Furthermore, we prove the Hyers-Ulam stability results for fixed point problems via C^*-algebra-valued extended quasi b-metric space.

• Journal for History of Mathematics
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• v.22 no.4
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• pp.129-144
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• 2009

The purpose of this study is what exactly De Morgan contributed to abstract algebra and mathematical logic. He recognised the purely symbolic nature of algebra and was aware of the existence of algebras other than ordinary algebra. He madealgebra as a science by introducing the ordered field and made the base for abstract algebra. He was one of the reformer of classical mathematical logic. Looking into De Morgan's works, we made it clear that the developments of algebra and mathematical logic in 19C.