# 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.

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Main Subjects

### History

• Receive Date: 15 December 2011
• Revise Date: 04 March 2012
• Accept Date: 12 April 2012