Abstract
Projective, injective, and global dimensions.The projective and injective dimensions of a moduleMwill be denoted by p.dim(M) and inj dim(M), respectively. Theright global dimensionof a ringR, denoted r.gl.dim(R), is the supremum of the projective dimensions of the right R-modules. Theleft global dimensionis defined analogously. Recall that the right and left global dimensions of a noetherian ring coincide[190,Corollary 9.23]. Hence, we just write gl.dim(R) for this dimension. It is also known that if inj.dim(RR) and inj.dim(RR) are both finite, then these numbers coincide[216,Lemma A]. In this case, we just write inj.dim(R) for the common value.
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© 2002 Springer Basel AG
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Brown, K.A., Goodearl, K.R. (2002). Homological Conditions. In: Lectures on Algebraic Quantum Groups. Advanced Courses in Mathematics CRM Barcelona. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8205-7_15
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DOI: https://doi.org/10.1007/978-3-0348-8205-7_15
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-6714-5
Online ISBN: 978-3-0348-8205-7
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