Peirce decompositions, idempotents and rings

[摘要] Idempotents dominate the structure theory of rings. The Peirce decomposition induced by an idempotent provides a natural environment for defining and classifying new types of rings. This point of view offers a way to unify and to expand the classical theory of semiperfect rings and idempotents to much larger classes of rings. Examples and applications are included. (C) 2020 Elsevier Inc. All rights reserved.

[发布日期] 2020-12-15

[关键词] Idempotent;Peirce decomposition;Peirce trivial;n-Peirce ring;Generalized matrix ring;Morita context;J-trivial;B-trivial