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1998•Journal of the London Mathematical SocietyOpen access

Non-Commutative Graded Homological Identities

Peter Jørgensen

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Abstract

Two results, the Auslander–Buchsbaum and Bass Theorems from the homological theory of commutative noetherian rings, are generalized to important classes of non-commutative N-graded algebras over fields. As a corollary to the generalized Auslander–Buchsbaum Theorem, it is found that under weak (so-called χ−) conditions, a non-commutative N-graded connected noetherian algebra of finite global dimension is in fact Artin–Schelter regular.

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What this paper is about

Two results, the Auslander–Buchsbaum and Bass Theorems from the homological theory of commutative noetherian rings, are generalized to important classes of non-commutative N-graded algebras over fields. As a corollary to the generalized Auslander–Buchsbaum Theorem, it is found that under weak (so-called χ−) conditions, a non-commutative N-graded connected noetherian algebra of finite global dimension is in fact Artin–Schelter regular.

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Available abstract

Two results, the Auslander–Buchsbaum and Bass Theorems from the homological theory of commutative noetherian rings, are generalized to important classes of non-commutative N-graded algebras over fields. As a corollary to the generalized Auslander–Buchsbaum Theorem, it is found that under weak (so-called χ−) conditions, a non-commutative N-graded connected noetherian algebra of finite global dimension is in fact Artin–Schelter regular.

Key concepts: Noetherian, Commutative property, Mathematics, Global dimension, Pure mathematics, Corollary, Local ring, Noetherian ring

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