• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.31-35
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• 2020

With the motivation to extend the Zelasko's theorem on commutative algebras, it was shown in [2] that if n ∈ {3, 4} is fixed, A, B are commutative algebras and h : A → B is an n-Jordan homomorphism, then h is an n-ring homomorphism. In this paper, we extend this result for all n ≥ 3.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.865-876
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• 2021

Let 𝔽 be a commutative ring. A restricted skew polynomial extension over 𝔽 is a class of iterated skew polynomial 𝔽-algebras which include well-known quantized algebras such as the quantum algebra U_q(𝔰𝔩₂), Weyl algebra, etc. Here we obtain a necessary and sufficient condition in order to be restricted skew polynomial extensions over 𝔽. We also introduce a restricted Poisson polynomial extension which is a class of iterated Poisson polynomial algebras and observe that a restricted Poisson polynomial extension appears as semiclassical limits of restricted skew polynomial extensions. Moreover, we obtain usual as well as unusual quantized algebras of the same Poisson algebra as applications.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.737-746
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• 1999

For a locally compact Abelian group G, and a commutative Banach algebra B, let $L^1$(G, B) be the Banach algebra of all Bochner integrable functions. We show that if G is noncompact and B is a semiprime Banach algebras in which every minimal prime ideal is cnotained in a regular maximal ideal, then $L^1$(G, B) contains no nontrivial separating idal. As a consequence we deduce some automatic continuity results for $L^1$(G, B).

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.375-384
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• 2009

Characterizations of simulative WFI-algebras are provided. The notion of commutators, doubly simulative parts, doubly simulative WFI-algebras, and WFI-morphisms are introduced. Using the notion of commutators, the conditions for a WFI-algebra to be simulative are given. Characterizations of doubly simulative WFI-algebras are discussed. Using the notion of doubly simulative WFI-algebras, a commutative pomonoid is established.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.251-256
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• 1997

We show that a strong system of derivations ${D_0, D_1,\cdots,D_m}$ on a commutative Banach algebra A is contained in the radical of A if it satisfies one of the following conditions for separating spaces; (1) $\partial(D_i) \subseteq rad(A) and \partial(D_i) \subseteq K D_i(rad(A))$ for all i, where $K D_i(rad(A)) = {x \in rad(A))$ : for each $m \geq 1, D^m_i(x) \in rad(A)}$. (2) $(D^m_i) \subseteq rad(A)$ for all i and m. (3) $\bar{x\partial(D_i)} = \partial(D_i)$ for all i and all nonzero x in rad(A).

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1481-1494
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• 2013

The paper is devoted to the study of finite dimensional complex evolution algebras. The class of evolution algebras isomorphic to evolution algebras with Jordan form matrices is described. For finite dimensional complex evolution algebras the criterium of nilpotency is established in terms of the properties of corresponding matrices. Moreover, it is proved that for nilpotent $n$-dimensional complex evolution algebras the possible maximal nilpotency index is $1+2^{n-1}$.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.189-195
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• 2014

Let X be a compact metric space, B be a unital commutative Banach algebra and ${\alpha}{\in}(0,1]$. In this paper, we first define the vector-valued (B-valued) ${\alpha}$-Lipschitz operator algebra $Lip_{\alpha}$ (X, B) and then study its structure and characterize of its maximal ideal space.

• Honam Mathematical Journal
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• v.41 no.4
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• pp.697-705
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• 2019

The article studies the concept of a (𝜑, 𝜓)-biflat and (𝜑, 𝜓)-amenable Banach algebra A, where 𝜑 is a continuous homomorphism on A and 𝜓 ∈ Φ_A. We show if A has a (𝜑, 𝜓)-virtual diagonal, then A is (𝜑, 𝜓)- biflat. In the case where 𝜑(A) is commutative we prove that (𝜑, 𝜓)- biflatness of A implies that A has a (𝜑, 𝜓)-virtual diagonal.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.305-317
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• 2000

It is well-known that every derivation on a commutative Banach algebra maps into its radical. In this paper we shall give the various algebraic conditions on the ring that every Jordan derivation on a noncommutative ring with suitable characteristic conditions is zero and using this result, we show that every continuous linear Jordan derivation on a noncommutative Banach algebra maps into its radical under the suitable conditions.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.443-450
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• 2011

In this paper, we construct a Gorenstein Artinian algebra R/J with non-unimodal Hilbert function h = (1, 13, 12, 13, 1) to investigate the algebraic structure of the ideal J in a polynomial ring R. For this purpose, we use a software system Macaulay 2, which is devoted to supporting research in algebraic geometry and commutative algebra.