• Kyungpook Mathematical Journal
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• 제63권4호
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• pp.551-560
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• 2023

In this paper we consider a more general class of centralizers called I-centralizers. More precisely, given a prime ideal P of an arbitrary ring R we establish a connection between certain algebraic identities involving a pair of P-left centralizers and the structure of the factor ring R/P.

• Korean Journal of Mathematics
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• 제17권4호
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• pp.437-449
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• 2009

In this paper, we establish the stability of cubic double centralizers and cubic multipliers on Banach algebras. We also prove the superstability of cubic double centralizers on Banach algebras which are cubic commutative and cubic without order.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.217-227
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• 2005

Let G be a finite group and $\#$Cent(G) denote the number of centralizers of its elements. G is called n-centralizer if $\#$Cent(G) = n, and primitive n-centralizer if $\#$Cent(G) = $\#$Cent($\frac{G}{Z(G)}$) = n. In this paper we investigate the structure of finite groups with at most 21 element centralizers. We prove that such a group is solvable and if G is a finite group such that G/Z(G)$\simeq$$A_5$, then $\#$Cent(G) = 22 or 32. Moreover, we prove that As is the only finite simple group with 22 centralizers. Therefore we obtain a characterization of As in terms of the number of centralizers

• 대한수학회지
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• 제47권3호
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• pp.523-535
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• 2010

In this paper, we show that Jordan $\tau$-centralizers and local $\tau$-centralizers are $\tau$-centralizers under certain conditions. We also discuss a new type of generalized derivations associated with Hochschild 2-cocycles and introduce a special local generalized derivation associated with Hochschild 2-cocycles. We prove that if $\cal{L}$ is a CDCSL and $\cal{M}$ is a dual normal unital Banach $alg\cal{L}$-bimodule, then every local generalized derivation of above type from $alg\cal{L}$ into $\cal{M}$ is a generalized derivation.

• 대한수학회보
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• 제52권2호
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• pp.367-376
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• 2015

In this paper, we classified finite p-groups G such that $$C_G(x)/<x>$$ is cyclic for all non-central elements $x{\in}G$. This solved a problem proposed By Y. Berkovoch.

• Kyungpook Mathematical Journal
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• 제22권2호
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• pp.303-307
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• 1982

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.403-410
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• 2006

For a finite group G, #Cent(G) denotes the number of centralizers of its elements. A group G is called n-centralizer if #Cent(G) = n, and primitive n-centralizer if #Cent(G) = #Cent($\frac{G}{Z(G)}$) = n. The first author in [1], characterized the primitive 6-centralizer finite groups. In this paper we continue this problem and characterize the primitive 7-centralizer finite groups. We prove that a finite group G is primitive 7-centralizer if and only if $\frac{G}{Z(G)}{\simeq}D_{10}$ or R, where R is the semidirect product of a cyclic group of order 5 by a cyclic group of order 4 acting faithfully. Also, we compute #Cent(G) for some finite groups, using the structure of G modulu its center.

• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.115-124
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• 2000

For a finite group G, #Cent(G) denotes the number of cen-tralizers of its clements. A group G is called n-centralizer if #Cent( G) = n. and primitive n-centralizer if #Cent(G) = #Cent(${\frac}{G}{Z(G)$) = n. In this paper we compute the number of distinct centralizers of some finite groups and investigate the structure of finite groups with Qxactly SLX distinct centralizers. We prove that if G is a 6-centralizer group then ${\frac}{G}{Z(G)$${\cong}D_8$,$A_4$, $Z_2{\times}Z_2{\times}Z_2$ or $Z_2{\times}Z_2{\times}Z_2{\times}Z_2$.

• 호남수학학술지
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• 제36권3호
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• pp.505-517
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• 2014

We prove that every Jordan higher left (right) centralizer on a 2-torsion free semiprime ring is a higher left (right) centralizer which is to generalize the result of Zalar [18].

• Kyungpook Mathematical Journal
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• 제56권1호
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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.