JP Journal of Algebra, Number Theory and Applications
Volume 31, Issue 2, Pages 75 - 90
(December 2013)
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REPRESENTATION OF ENDOMORPHISMS OF A MODULE OVER A VALUATION DOMAIN
Hiroyuki Ishibashi
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Abstract: We study a representation of an arbitrary endomorphism son a free module Mof a finite rank nover a valuation domain R, that is, factorize Minto a direct sum of some free submodules determined by s, give a sufficient condition for sto have the rational canonical form, find a basis for Mover Rrelative to which the matrix of sis a sum of a lower triangular matrix and a super diagonal matrix, and show that for some simple ring extension of Rthe natural prolongation of shas the rational canonical form. |
Keywords and phrases: rational canonical form, system of invariants, Jordan normal form, minimal polynomial, characteristic polynomial, endomorphism ring of a module, classical groups. |
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