Talk:Krull–Schmidt category
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Finite dimensional[edit]
I think one often talks about rings where the Krull-Schmidt property holds for finitely generated modules (like Reiner's Maximal Orders, and lots of chapters on p-modular systems), but I don't normally see the category property given a name.
For finite dimensional vector spaces over a field considered as modules over some ring, endo is a local ring iff it has no nonzero idempotents. That is, strongly indecomposable = indecomposable. I'm not sure how this behaves in subcategories, etc.
Is there a source for this article? I can bring lots of nice material on Krull-Schmidt properties either in the reps of finite groups context or in the context of non-commutative rings, but I want to make sure I am putting it on the right page. JackSchmidt (talk) 19:51, 16 January 2009 (UTC)
I created this page because I initially ran into them in this article: http://arxiv.org/abs/math.RT/0402054 The book I looked at for the relevant definitions is the one by Ringel, Tame Algebras and Integral Quadratic Forms that I put in the references. See in particular section 2.2. So I've only seen these categories given such a name in the context of finite-dimensional algebras. Masnevets (talk) 23:16, 16 January 2009 (UTC)