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Products of idempotent integer matrices

Published online by Cambridge University Press:  24 October 2008

John Fountain
John Fountain
Affiliation:
Department of Mathematics, University of York, Heslington, York YO1 5DD
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Abstract

Let E denote the set of non-identity idempotent matrices in the full matrix ring Mn(R) over a principal ideal domain R. A necessary and sufficient condition is found for the subsemigroup generated by E to be the set of all matrices in Mn(R) of rank less than n. The condition is satisfied when R is a discrete valuation ring and when R is the ring of integers. Thus every n × n matrix of rank less than n is a product of idempotent integer matrices.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 3 , November 1991 , pp. 431 - 441
Copyright
Copyright © Cambridge Philosophical Society 1991

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