• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.121-123
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• 2016

In this paper, we compute the number of distinct centralizers and commutativity degree of a class of finite groups. These computations produce a further class of examples of groups answering one question raised by Belcastro and Sherman and another one raised by Lescot.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.37-44
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• 2018

We prove some theorems showing that a right Jordan ideal or a left Jordan ideal of a 3-prime near-ring must be commutative if it admits a nonzero derivation acting as a homomorphism or an antihomomorphism. Moreover, we give examples proving necessity of the conditions given.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.915-923
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• 2022

The purpose of the present paper is to obtain commutativity of prime Γ-near-ring N with generalized derivations F and G with associated derivations d and h respectively satisfying one of the following conditions:(i) G([x, y]α = ±f(y)α(xoy)βγg(y), (ii) F(x)βG(y) = G(y)βF(x), for all x, y ∈ N, β ∈ Γ (iii) F(u)βG(v) = G(v)βF(u), for all u ∈ U, v ∈ V, β ∈ Γ,(iv) if 0 ≠ F(a) ∈ Z(N) for some a ∈ V such that F(x)αG(y) = G(y)αF(x) for all x ∈ V and y ∈ U, α ∈ Γ.

• Kyungpook Mathematical Journal
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• v.43 no.4
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• pp.499-502
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• 2003

The aim of the present paper is to establish for commutativity of rings with unity 1 satisfying one of the properties $(xy)^{k+1}=x^ky^{k+1}x$ and $(xy)^{k+1}=yx^{k+1}y^k$, for all x, y in R, and the mapping $x{\rightarrow}x^k$ is an anti-homomorphism where $k{\geq}1$ is a fixed positive integer.

• Journal of the Korean Mathematical Society
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• v.46 no.3
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• pp.621-642
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• 2009

In this paper we give necessary and sufficient conditions that two Toeplitz operators with monomial symbols acting on the weighted Bergman space commute. We also present necessary and sufficient conditions for the hyponormality of Toeplitz operators with some special symbols on the weighted Bergman space. All the results are stated in terms of the Mellin transform of the symbol.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.433-445
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• 2016

In the present paper, we expand the domain of work on the concept of semiderivations in 3-prime near-rings through the study of structure and commutativity of near-rings admitting semiderivations satisfying certain differential identities. Moreover, several examples have been provided at places which show that the assumptions in the hypotheses of various theorems are not altogether superfluous.

• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.711-713
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• 2006

Let R be a semiprime ring and f be an endomorphism on R. If f is a strong commutativity preserving (simply, scp) map on a non-zero ideal U of R, then f is commuting on U.

• The Pure and Applied Mathematics
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• v.10 no.3
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• pp.145-161
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• 2003

Weak commutativity of a pair of maps was introduced by Sessa [On a weak commutativity condition of mappings in fixed point considerations. Publ. Inst. Math. (Beograd) (N.S.) 32(40) (1982),149-153] in fixed point considerations. Thereafter a number of generalizations of this notion has been obtained. The purpose of this paper is to present a brief development of weaker forms of commuting maps, and to obtain two fixed point theorems for noncommuting and noncontinuous maps on noncomplete metric spaces.

• Bulletin of the Korean Mathematical Society
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• v.43 no.1
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• pp.101-106
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• 2006

Let R be a prime ring and I a nonzero ideal of R. Let $\alpha,\;\nu,\;\tau\;R{\rightarrow}R$ be the endomorphisms and $\beta,\;\mu\;R{\rightarrow}R$ the automorphisms. If R admits a generalized $(\alpha,\;\beta)-derivation$ g associated with a nonzero $(\alpha,\;\beta)-derivation\;\delta$ such that $g([\mu(x),y])\;=\;[\nu/(x),y]\alpha,\;\tau$ for all x, y ${\in}I$, then R is commutative.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.461-472
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• 2021

We study a new ring property called axis-commutativity. Axis-commutative rings are seated between commutative rings and duo rings and are a generalization of division rings. We investigate the basic structure and several extensions of axis-commutative rings.