Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Idempotents in matrix rings


Authors: Christopher Barnett and Victor Camillo
Journal: Proc. Amer. Math. Soc. 122 (1994), 965-969
MSC: Primary 16S50; Secondary 15A99, 16E50
MathSciNet review: 1246513
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let R be a commutative, von Neumann regular ring and $ {M_n}(R)$ the ring of $ n \times n$ matrices over R. What are the idempotents in $ {M_n}(R)$ ? Our motivation is to think of R as the sort of ring that occurs in functional analysis, for example a ring of measurable functions. We show how to uniquely write down all idempotents in $ {M_n}(R)$ in terms of arbitrary parameters. The main theorem is stated in language to appeal to an audience wider than algebraists, but in a remark, we give a more refined statement for specialists.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16S50, 15A99, 16E50

Retrieve articles in all journals with MSC: 16S50, 15A99, 16E50


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1246513-1
PII: S 0002-9939(1994)1246513-1
Article copyright: © Copyright 1994 American Mathematical Society