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I am looking for examples of indecomposable rings with nontrivial idempotents. The only examples I can think of are matrix rings. Are there other examples?

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    http://planetmath.org/encyclopedia/Idempotent2.html2011-09-25
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    @FrankMurphy Would you mind to work out your comment?2012-07-12
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    Just that a non-trivial descomposition of a ring correspond to a set of non.trivial idempotents elements, so if you have a non-trivial idempotent you´ll have a descomposition of a your ring.2012-07-14
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    definition of indecomposable ring?2012-09-18

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