When is a regular local ring a locality?

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

‎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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ژورنال

عنوان ژورنال: Journal of Algebra

سال: 1988

ISSN: 0021-8693

DOI: 10.1016/0021-8693(88)90035-x