Homological Dimension of Skew Group Rings and Crossed Products

✍ Scribed by Z. Yi

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 888 KB
• Volume: 164
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1994.1056

✦ Synopsis

In this paper we study the homological dimension of skew group rings and crossed products. A sufficient condition for (R * G), a crossed product, to have finite right global dimension is given, in terms of crossed products over simple Artinian factors of (R) if (R) is right FBN and left coherent and (G) is finite. Some necessary conditions and sufficient conditions for (R * G), a skew group ring of a finite group over a local or semilocal right Noetherian ring, to have finite right global dimension are also given. Then in particular if (R) is commutative Noetherian and (G) is finite, we obtain some equivalent conditions for (R * G), a skew group ring, to have finite global dimension. Using work of Aljadeff [E. Aljadeff, Serre's extension theorem for crossed products, J. London Math. Soc. 44 (1991), 47-54], these results are extended to polycyclic-by-finite groups. 1994 Academic Press. Inc.