The Restricted Linear Group

  • F. E. A. JohnsonEmail author
Part of the Algebra and Applications book series (AA, volume 17)


A celebrated result of H.J.S. Smith (Jacobson in Basic algebra. Freeman, New York, 1974, Smith in Philos. Trans. 151:293:326, 1861) shows that when Λ is a commutative integral domain which possesses a Euclidean algorithm then an arbitrary m×m matrix X over Λ can be expressed as a product X=E + DE where D is diagonal and E +, E are products of elementary unimodular matrices. This chapter is a general study of rings whose matrices possess an analogue of such a Smith Normal Form.


Smith Normal Form Commutative Integral Domain Strong Lifting Property Weak Determinant Surjective Ring Homomorphism 
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Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity College LondonLondonUK

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