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1983•Glasgow Mathematical JournalOpen access

A class of maximal orders integral over their centres

Andy J. Gray

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Abstract

In a recent paper [1], Brown, Hajarnavis and MacEacharn have considered non-commutative Noetherian local rings of finite global dimension which are integral over their centres. For such a ring Rthey have shown: (i) R is a prime ring whose Krull and global dimensions coincide; (ii) R = ∩ RP where p runs through the set of rank one primes of the centre of R, and each Rp is hereditary; (iii) the centre of R is a Krull domain.

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In a recent paper [1], Brown, Hajarnavis and MacEacharn have considered non-commutative Noetherian local rings of finite global dimension which are integral over their centres. For such a ring Rthey have shown: (i) R is a prime ring whose Krull and global dimensions coincide; (ii) R = ∩ RP where p runs through the set of rank one primes of the centre of R, and each Rp is hereditary; (iii) the centre of R is a Krull domain.

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Available abstract

In a recent paper [1], Brown, Hajarnavis and MacEacharn have considered non-commutative Noetherian local rings of finite global dimension which are integral over their centres. For such a ring Rthey have shown: (i) R is a prime ring whose Krull and global dimensions coincide; (ii) R = ∩ RP where p runs through the set of rank one primes of the centre of R, and each Rp is hereditary; (iii) the centre of R is a Krull domain.

Key concepts: Krull dimension, Mathematics, Integral domain, Regular local ring, Global dimension, Noetherian ring, Noetherian, Commutative ring

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