• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.487-490
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• 2023

In this short note, we give a simple proof of the main theorem of [5] which states that every n-Jordan homomorphism h : A → B between two commutative algebras A and B is an n-homomorphism.

• 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.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.293-303
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• 2015

In this paper, we shall introduce the concept of rough antifuzzy subring and prove some theorems in this context. We have, if µ is an anti-fuzzy subring, then µ is a rough anti-fuzzy subring. Also we give some properties of homomorphism and anti-homomorphism on rough anti-fuzzy subring.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.427-436
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• 2011

In this paper, we first show that the pull-back morphism between two K-groups of the Steinberg varieties, obtained respectively from partial flag varieties and quiver varieties of type A, is a ring homomorphism with respect to the convolution product. Then, we prove that this ring homomorphism yields a property of compatibility between two certain convolution actions.

• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.497-505
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• 2021

Let R → S be a ring homomorphism. The relations of Gorenstein projective dimension with respect to a semidualizing module of homologically bounded complexes between U ⊗LR X and X are considered, where X is an R-complex and U is an S-complex. Some sufficient conditions are given under which the equality ${\mathcal{GP}}_{\tilde{C}}-pd_S(S{\otimes}{L \atop R}X)={\mathcal{GP}}_C-pd_R(X)$ holds. As an application it is shown that the Auslander-Buchsbaum formula holds for GC-projective dimension.

• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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• pp.725-743
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• 2022

In this paper, the concepts of ω-linked homomorphisms, the ω_𝜙-operation, and DW_𝜙 rings are introduced. Also the relationships between ω_𝜙-ideals and ω-ideals over a ω-linked homomorphism 𝜙 : R → T are discussed. More precisely, it is shown that every ω_𝜙-ideal of T is a ω-ideal of T. Besides, it is shown that if T is not a DW_𝜙 ring, then T must have an infinite number of maximal ω_𝜙-ideals. Finally we give an application of Cohen's Theorem over ω-factor rings, namely it is shown that an integral domain R is an SM-domain with ω-dim(R) ≤ 1, if and only if for any nonzero ω-ideal I of R, (R/I)_ω is an Artinian ring, if and only if for any nonzero element α ∈ R, (R/(a))_ω is an Artinian ring, if and only if for any nonzero element α ∈ R, R satisfies the descending chain condition on ω-ideals of R containing a.

• Journal of the Korean Mathematical Society
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• v.53 no.2
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• pp.381-401
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• 2016

According to Jacobson [31], a right ideal is bounded if it contains a non-zero ideal, and Faith [15] called a ring strongly right bounded if every non-zero right ideal is bounded. From [30], a ring is strongly right AB if every non-zero right annihilator is bounded. In this paper, we introduce and investigate a particular class of McCoy rings which satisfy Property (A) and the conditions asked by Nielsen [42]. It is shown that for a u.p.-monoid M and ${\sigma}:M{\rightarrow}End(R)$ a compatible monoid homomorphism, if R is reversible, then the skew monoid ring R * M is strongly right AB. If R is a strongly right AB ring, M is a u.p.-monoid and ${\sigma}:M{\rightarrow}End(R)$ is a weakly rigid monoid homomorphism, then the skew monoid ring R * M has right Property (A).

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1095-1106
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• 2020

The purpose of this paper is to introduce a new class of rings that is closely related to the class of pseudo-Krull domains. Let 𝓗 = {R | R is a commutative ring and Nil(R) is a divided prime ideal of R}. Let R ∈ 𝓗 be a ring with total quotient ring T(R) and define 𝜙 : T(R) → R_Nil(R) by ${\phi}({\frac{a}{b}})={\frac{a}{b}}$ for any a ∈ R and any regular element b of R. Then 𝜙 is a ring homomorphism from T(R) into R_Nil(R) and 𝜙 restricted to R is also a ring homomorphism from R into R_Nil(R) given by ${\phi}(x)={\frac{x}{1}}$ for every x ∈ R. We say that R is a 𝜙-pseudo-Krull ring if 𝜙(R) = ∩ R_i, where each R_i is a nonnil-Noetherian 𝜙-pseudo valuation overring of 𝜙(R) and for every non-nilpotent element x ∈ R, 𝜙(x) is a unit in all but finitely many R_i. We show that the theories of 𝜙-pseudo Krull rings resemble those of pseudo-Krull domains.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2027-2034
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• 2013

In this article, it is proved that under some conditions every bijective Jordan triple product homomorphism from generalized matrix algebras onto rings is additive. As a corollary, we obtain that every bijective Jordan triple product homomorphism from $M_n(\mathcal{A})$ ($\mathcal{A}$ is not necessarily a prime algebra) onto an arbitrary ring $\mathcal{R}^{\prime}$ is additive.

• East Asian mathematical journal
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• v.36 no.1
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• pp.101-114
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• 2020

In this paper, we investigate commutativity of semiprime rings with a derivation which is strongly commutativity preserving and acts as a homomorphism or as an anti-homomorphism on a nonzero Lie ideal.