HALF-ORTHOGONAL SETS OF IDEMPOTENTS

Victor P Camillo; Pace P Nielsen

doi:10.1090/tran/6350

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HALF-ORTHOGONAL SETS OF IDEMPOTENTS

Victor P Camillo and Pace P Nielsen

Transactions of the American Mathematical Society, Vol.368(2), pp.965-987

02/01/2016

DOI: 10.1090/tran/6350

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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.

Mathematics

Physical Sciences

Science & Technology

Details

Title: Subtitle: HALF-ORTHOGONAL SETS OF IDEMPOTENTS
Creators: Victor P Camillo - University of Iowa
Pace P Nielsen - Brigham Young University
Resource Type: Journal article
Publication Details: Transactions of the American Mathematical Society, Vol.368(2), pp.965-987
DOI: 10.1090/tran/6350
ISSN: 0002-9947
eISSN: 1088-6850
Publisher: American Mathematical Society
Number of pages: 23
Grant note: 315828 / Simons Foundation
Language: English
Date published: 02/01/2016
Academic Unit: Mathematics
Record Identifier: 9984240762602771

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