Half-orthogonal sets of idempotents

Camillo, Victor; Nielsen, Pace

doi:10.1090/tran/6350

Half-orthogonal sets of idempotents
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by Victor P. Camillo and Pace P. Nielsen PDF

Trans. Amer. Math. Soc. 368 (2016), 965-987 Request permission

Abstract:

We improve several results in the literature focused on lifting idempotents, by either removing the lifting hypothesis or weakening other assumptions. We prove that countable sets of idempotents, which are orthogonal modulo an enabling ideal, lift to orthogonal idempotents. Left associates of liftable idempotents also lift modulo the Jacobson radical. Additionally, we exhibit situations when half-orthogonal sets of idempotents can be orthogonalized by multiplying by a unit. We finish by proving a number of results on directs sums of modules with the exchange property.

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