Peirce decompositions, idempotents and rings
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2017
- DOI:
- 10.48550/arXiv.1702.05261
- arXiv:
- arXiv:1702.05261
- Bibcode:
- 2017arXiv170205261A
- Keywords:
-
- Mathematics - Rings and Algebras;
- 16S50;
- 15A33;
- 16D20;
- 16D70