DUBROVIN VALUATION PROPERTIES OF SKEW GROUP-RINGS AND CROSSED-PRODUCTS

In this paper some conditions for a skew group ring or a crossed produ ct to have finite weak global dimension are given. Using these results we obtain some necessary conditions and some sufficient conditions fo r a skew group ring or a crossed product to be a Dubrovin valuation ri ng. If RG is a skew group ring, where the coefficient ring R is a com mutative ring and G is a finite group, then we prove that the conditio ns we obtained become necessary and sufficient conditions. In particul ar, if R is a commutative valuation ring, then RG is a Dubrovin valua tion ring if and only if G(T) = < 1 >, where G(T) is the inertial grou p of R.