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Lifting maximal orders. (English) Zbl 0663.16004
The reviewer, generalizing a result of G. Maury [Commun. Algebra 14, 1515–1517 (1986; Zbl 0601.16005)], proved that if \(P\) is an invertible ideal contained in the Jacobson radical of a Noetherian ring \(R\) such that \(R/P\) is a maximal order in a simple Artinian ring, then \(R\) is a maximal order in a simple Artinian ring [the reviewer, Commun. Algebra 17, 331–339 (1989; see the preceding review Zbl 0663.16003)]. The authors extend this result to filtered rings and show that, under suitable conditions, if \(R\) is a filtered ring with associated graded ring \(G(R)\) such that \(G(R)\) is a maximal order in a simple Artinian ring, then \(R\) is also a maximal order in a simple Artinian ring.

MSC:
16H05 Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)
16W50 Graded rings and modules (associative rings and algebras)
16Kxx Division rings and semisimple Artin rings
16P50 Localization and associative Noetherian rings
16N60 Prime and semiprime associative rings
16P40 Noetherian rings and modules (associative rings and algebras)
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References:
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