Centrality and Partition of Idempotents

2023/07/07 by Chintala, Vineeth
#05C25 #16B99 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2311.08404

Abstract

We show that an idempotent lies in the center if it commutes with the other idempotents in the ring. Next, we introduce a partition of the set of idempotents and show that the automorphisms of the ring act transitively on each equivalence class.

Related

• A note on semicentral Idempotents
• Peirce decompositions, idempotents and rings
• On idempotents of a class of commutative rings
• The centralizer of an element in an endomorphism ring
• A Note on Idempotent Matrices: The Poset Structure and The Construction