When is the ring of real measurable functions a hereditary ring?

Document Type: Research Paper

Authors

Department of Mathematical Sciences‎, ‎Shahrekord‎ ‎University‎, ‎P.O. Box 115‎, ‎Shahrekord‎, ‎Iran.

Abstract

‎Let $M(X‎, ‎\mathcal{A}‎, ‎\mu)$ be the ring of real-valued measurable functions‎ ‎on a measure space $(X‎, ‎\mathcal{A}‎, ‎\mu)$‎. ‎In this paper‎, ‎we characterize the maximal ideals in the rings of real measurable functions‎ ‎and as a consequence‎, ‎we determine when $M(X‎, ‎\mathcal{A}‎, ‎\mu)$ is a hereditary ring.

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Main Subjects


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Volume 43, Issue 6
November and December 2017
Pages 1905-1912
  • Receive Date: 01 June 2015
  • Revise Date: 19 November 2016
  • Accept Date: 23 November 2016