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Unformatted text preview: mations T i have a simple form. Because V is a nitely generated torsion module over the Euclidean domain Kx , according to Theorem 8.5.2 , .T;V / has a direct sum decomposition .T;V / D .T 1 ;V 1 / .T s ;V s /; where V i is a cyclic Kx module V i Kx=.a i .x//; deg .a i .x// 1 (that is, a i .x/ is not zero and not a unit) and a i .x/ divides a j .x/ if i j . Moreover, if we insist that the a i .x/ are monic, then they are unique. We call the polynomials a i .x/ the invariant factors of T . To understand the structure of T , it sufces to understand how T i acts on the cyclic Kx module V i ....
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This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
 Fall '08
 EVERAGE
 Algebra

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