Let R be a principal ideal domain. For each positive integer rand sequence of nonzero ideals I
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Let R be a principal ideal domain. For each positive integer rand sequence of nonzero ideals I1 ⊃ I2 ⊃ • . • ⊃ Ir choose a sequence d1, ... , dr ϵ R such that (dj) = Ij and d1| d2 I· · · I dr. For a given pair of positive integers (n, m), let S be these to fall n X m matrices of the for m where r = 1, 2, ... ,min(n, m) and L, is an r X r diagonal matrix with main diagonal one of the chosen sequences d1, . .. , dr. Show that S is a set of canonical forms under equivalence for the set of all n X m matrices over R.
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Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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