This article is cited in 1 paper

On the Ranks of Idempotent Matrices over Skew Semifields

S. N. Il'in

Kazan (Volga Region) Federal University

Abstract: As is well known, every positive idempotent matrix is of rank 1. It is proved that idempotent matrices without zeros have this property over many skew semifields, and all these skew semifields are described.

Keywords: idempotent matrix, rank, skew semifield, (weakly) additively idempotent skew semifield, (weakly) additively cancellable skew semifield.

UDC: 512.558+512.643

Received: 27.05.2010
Revised: 19.03.2011

DOI: 10.4213/mzm8884

 English version: Mathematical Notes, 2012, 91:6, 782–788

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