Register to reply

A question about invariant factors...

by Artusartos
Tags: factors, invariant
Share this thread:
Jan16-13, 10:20 AM
P: 248
A Theorem in our textbook says...

If R is a PID, then every finitely generated torision R-module M is a direct sum of cyclic modules

[tex]M= R/(c_1) \bigoplus R/(c_2) \bigoplus ... \bigoplus R/(c_t)[/tex]

where [tex]t \geq 1[/tex] and [tex]c_1 | c_2 | ... | c_t [/tex].

There is an example from our textbook that I attached...they find the invariant factors from the elementary divisors. But what if we had to find the invariant factors without being given the elementary divisors. How would we do that?

Thanks in advance
Attached Thumbnails
644.jpg   645.jpg  
Phys.Org News Partner Science news on
Scientists discover RNA modifications in some unexpected places
Scientists discover tropical tree microbiome in Panama
'Squid skin' metamaterials project yields vivid color display
Jan18-13, 03:00 PM
Sci Advisor
HW Helper
mathwonk's Avatar
P: 9,498
well you have to be given something. i have some examples in my book on my webpage.

to be "given" a f.g. module usually means to be given a "presentation" as a quotient of two free modules.

such a quotient is specified by a matrix. then you diagonalize that presentation matrix.

see the discussion here:

Register to reply

Related Discussions
Lagrangian invariant but Action is gauge invariant Advanced Physics Homework 1
X-ray question about form factors Advanced Physics Homework 0
A question about factoring and factors Linear & Abstract Algebra 1
Invariant stress tensor = Invariant force? Advanced Physics Homework 0