Monatshefte für Mathematik

, Volume 165, Issue 3–4, pp 353–363

Matrix near-rings and 0-primitivity

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Abstract

In this article, we study the implication of the primitivity of a matrix near-ring \({\mathbb{M}_n(R) (n >1 )}\) and that of the underlying base near-ring R. We show that when R is a zero-symmetric near-ring with identity and \({\mathbb{M}_n(R)}\) has the descending chain condition on \({\mathbb{M}_n(R)}\)-subgroups, then the 0-primitivity of \({\mathbb{M}_n(R)}\) implies the 0-primitivity of R. It is not known if this is true when the descending chain condition on \({\mathbb{M}_n(R)}\) is removed. On the other hand, an example is given to show that this is not true in the case of generalized matrix near-rings.

Keywords

Primitive near-ring Matrix near-ring 

Mathematics Subject Classification (2000)

Primary 16Y30 Secondary 16N20 16S50 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of MathematicsNational Cheng Kung University, and National Center for Theoretical Sciences (South)TainanTaiwan
  2. 2.Department of Mathematics and Applied MathematicsUniversity of the Free StateBloemfonteinSouth Africa

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