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Homological Properties of Fully Bounded Noetherian Rings
Author(s) -
Teo KokMing
Publication year - 1997
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610796004620
Subject(s) - mathematics , noetherian , global dimension , bounded function , local ring , pure mathematics , quotient , ring (chemistry) , artinian ring , dimension (graph theory) , noncommutative ring , discrete mathematics , order (exchange) , simple (philosophy) , noetherian ring , radical of a ring , principal ideal ring , algebra over a field , commutative ring , commutative property , mathematical analysis , philosophy , chemistry , organic chemistry , finance , epistemology , economics
Let R be a fully bounded Noetherian ring of finite global dimension. Then we prove that K dim ( R ) ⩽ gldim ( R ). If, in addition, R is local, in the sense that R / J ( R ) is simple Artinian, then we prove that R is Auslander‐regular and satisfies a version of the Cohen–Macaulay property. As a consequence, we show that a local fully bounded Noetherian ring of finite global dimension is isomorphic to a matrix ring over a local domain, and a maximal order in its simple Artinian quotient ring.
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