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Maximal orders in Artinian rings. (English) Zbl 0541.16013
The two principal results of this paper concern a Noetherian ring R which is a maximal order in its Artinian quotient ring. The first states that R is a direct sum of prime rings and a ring S which contains no reflexive ideals other than S itself. Examples are given to show that S may be neither prime nor Artinian. The second result states: If T is a proper reflexive ideal of R then R/T has a quotient ring which is an Artinian principal ideal ring. This extends a result for prime rings R of M. Chamarie [J. Algebra 72, 210-222 (1981; Zbl 0468.16008)].
Reviewer: K.A.Brown

16P40 Noetherian rings and modules (associative rings and algebras)
16P50 Localization and associative Noetherian rings
16H05 Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)
16D70 Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras)
16Dxx Modules, bimodules and ideals in associative algebras
Full Text: DOI
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