define where is a cyclic group of prime order p, then R is a module over itself (it's a ring). If then I need to show that the set is an indecomposable module.

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- Jan 24th 2009, 03:46 AMPrometheusindecomposable module
define where is a cyclic group of prime order p, then R is a module over itself (it's a ring). If then I need to show that the set is an indecomposable module.

- Jan 24th 2009, 03:50 PMNonCommAlg
let note that is the augmentation ideal of and i'll show that is a minimal ideal of which solves the problem. it's clear that

now since we only need to prove that if is an ideal of such that then either or this is very easy to see:

since is a PID, we have for some since we have for some but which means for

some thus and hence but since is irreducible over we must have either or thus

either or - Jan 25th 2009, 06:18 AMPrometheus
"it's clear that http://www.mathhelpforum.com/math-he...e0a556a3-1.gif ..."

actually,as clear as it is, I didn't notice it. thanks, that was exactly what I missed