Hostname: page-component-76fb5796d-vfjqv Total loading time: 0 Render date: 2024-04-27T02:08:01.596Z Has data issue: false hasContentIssue false
  • English
  • Français

A Canonical Set For Matrices Over a Principal Ideal Ring Modulo m

Published online by Cambridge University Press:  20 November 2018

L. E. Fuller
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

If m ∈ P where P is a p.i.r. (principal ideal ring), then P/ {m} is a commutative ring with unit element. The elements of this ring are designated by ā where a ∈ P. The set of square matrices of order n with elements in P/ {m} forms a ring with unit element. The units in this ring are the unimodular matrices, i.e., the matrices whose determinants are units of P/ {m}.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 7 , 1955 , pp. 54 - 59
Copyright
Copyright © Canadian Mathematical Society 1955

References

1. Fuller, L. E., The Hermite canonical form for a matrix with elements in the ring of integers modulo m, Thesis, University of Wisconsin, 1950.Google Scholar
2. MacDuffee, C. C., Introduction to abstract algebra (New York, 1940).Google Scholar