On p-semilinear transformations

Document Type: Research Paper

Authors

1 Northeast Normal University

2 Department of Mathematics, Northeast Normal University

Abstract

In this paper, we introduce $p$-semilinear transformations for linear algebras over a field ${bf F}$ of positive
characteristic $p$, discuss initially the elementary properties of
$p$-semilinear transformations, make use of it to give some
characterizations of linear algebras over a field ${bf F}$ of
positive characteristic $p$. Moreover, we find a one-to-one
correspondence between $p$-semilinear transformations and matrices, and we prove a result which is closely related to the well-known Jordan-Chevalley decomposition of an element.

Keywords

Main Subjects



Volume 39, Issue 4
September and October 2013
Pages 725-742
  • Receive Date: 15 December 2011
  • Revise Date: 04 March 2012
  • Accept Date: 12 April 2012