• Title/Summary/Keyword: centralizers

Search Result 16, Processing Time 0.024 seconds

Commutativity Criteria for a Factor Ring R/P Arising from P-Centralizers

  • Lahcen Oukhtite;Karim Bouchannafa;My Abdallah Idrissi
    • Kyungpook Mathematical Journal
    • /
    • v.63 no.4
    • /
    • pp.551-560
    • /
    • 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.

CUBIC DOUBLE CENTRALIZERS AND CUBIC MULTIPLIERS

  • Lee, Keun Young;Lee, Jung Rye
    • Korean Journal of Mathematics
    • /
    • v.17 no.4
    • /
    • pp.437-449
    • /
    • 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.

  • PDF

ON FINITE GROUPS WITH A CERTAIN NUMBER OF CENTRALIZERS

  • REZA ASHRAFI ALI;TAERI BIJAN
    • Journal of applied mathematics & informatics
    • /
    • v.17 no.1_2_3
    • /
    • pp.217-227
    • /
    • 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

τ-CENTRALIZERS AND GENERALIZED DERIVATIONS

  • Zhou, Jiren
    • Journal of the Korean Mathematical Society
    • /
    • v.47 no.3
    • /
    • pp.523-535
    • /
    • 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.

ON FINITE GROUPS WITH EXACTLY SEVEN ELEMENT CENTRALIZERS

  • Ashrafi Ali-Reza;Taeri Bi-Jan
    • Journal of applied mathematics & informatics
    • /
    • v.22 no.1_2
    • /
    • pp.403-410
    • /
    • 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.

COUNTING THE CINTRALIZERS OF SOME FINITE GROUPS

  • Ashrafi, Ali Reza
    • Journal of applied mathematics & informatics
    • /
    • v.7 no.1
    • /
    • pp.115-124
    • /
    • 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 $Z_2{\times}Z_2{\times}Z_2{\times}Z_2$.