A partition of finite rings makes lifting possible

2020/09/26 by Vineeth Chintala, Chintala, Vineeth
Engineering · Mathematics · #05A18 #05C25 #16P10 #17A05 #Advanced Topics in Algebra #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2009.12508

openalex publication_date 2020/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that every finite ring has a partition, where each block corresponds to one idempotent. Remarkably, this partition provides a way to lift a wide variety of special elements such as idempotents, nilpotents, unipotents, roots of unity and regular elements.

Related

• Peirce decompositions, idempotents and rings
• Centrality and Partition of Idempotents
• Cardinality of groups and rings via the idempotency of infinite cardinals
• The unreasonable power of the lifting property in elementary mathematics
• Algebraic and Topological Results on Lifting Properties in Residuated Lattices