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Half-orthogonal sets of idempotents

Authors: Victor P. Camillo and Pace P. Nielsen
Journal: Trans. Amer. Math. Soc. 368 (2016), 965-987
MSC (2010): Primary 16U99; Secondary 16D70, 16N20
Published electronically: May 6, 2015
MathSciNet review: 3430355
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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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Additional Information

Victor P. Camillo
Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242

Pace P. Nielsen
Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602

Keywords: Exchange property, half-orthogonal, idempotents, Jacobson radical, semi-$T$-nilpotent
Received by editor(s): August 28, 2013
Received by editor(s) in revised form: December 11, 2013
Published electronically: May 6, 2015
Article copyright: © Copyright 2015 American Mathematical Society

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