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Title: Maximal zero product subrings and inner ideals of simple rings
Authors: Baranov, Alexander
Fernández López, Antonio
First Published: 31-Jul-2019
Award date: 18-Aug-2017
Publisher: Elsevier for Academic Press
Citation: Journal of Algebra, 2019
Abstract: Let Q be a (not necessarily unital) simple ring or algebra. A nonempty subset S of Q is said to have zero product if S 2 = 0. We classify all maximal zero product subsets of Q by proving that the map R 7→ R∩LeftAnn(R) is a bijection from the set of all proper nonzero annihilator right ideals of Q onto the set of all maximal zero product subsets of Q. We also describe the relationship between the maximal zero product subsets of Q and the maximal inner ideals of its associated Lie algebra.
DOI Link: 10.1016/j.jalgebra.2019.07.016
ISSN: 0021-8693
Embargo on file until: 31-Jul-2020
Version: Post-print
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © Elsevier for Academic Press 2019. After an embargo period this version of the paper will be an open-access article distributed under the terms of the Creative Commons Attribution-Non Commercial-No Derivatives License (, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
Description: The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.
Appears in Collections:Published Articles, Dept. of Mathematics

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