Completions of Noetherian hereditary prime rings

V. K. Deshpande

Vol. 90 (1980), No. 2, 285–297

DOI: 10.2140/pjm.1980.90.285

Abstract

If R is a Noetherian hereditary prime ring with Jacobson radical J≠(0) then, it has been shown that the J-adic completion of R is a Noetherian hereditary semi-prime ring; it is prime if and only if the maximal ideals of R form a single cycle. Among other things, one also finds the result: If R is a right Noetherian semi-local ring with ⋂ _n=1^∞Jⁿ = (0) then, R is J-adic complete if and only if it is right linearly compact and J has the right AR-property.

Mathematical Subject Classification

Primary: 16A12, 16A12

Secondary: 16A14

Milestones

Received: 18 July 1978

Revised: 26 September 1979

Published: 1 October 1980