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Graded Rings and Localizations
ShengGui Zhang
Acta Mathematica Sinica, Chinese Series
1998, 41 (1):
null-.
DOI: 10.12386/A1998sxxb0002
Suppose G is a finite group, R is a graded ring of type G with identity and S is a multiplicatively closed subset of the set consisting of all homogeneous elements of R. Let =x∈Gae(gx,x)a∈S, Deg (a)=g∈G] and S==x∈ G ae (gx,xh)a ∈S, Deg (a)=g∈ G, h∈ G. M G(R) denotes the matrices over R with the rows columns indexed by elements of G. In this paper, we prove that R satisfies the left Ore condition with S if and only if R# G satisfies the left Ore condition with if and only if M G(R) satisfies the left Ore condition with S=. Inaddition, we obtained the following results: -1 (R# G) is isomorphic to (S -1 R)# G and S=, -1 (M G(R)) is isomorphic to M G(S -1 R) as rings.
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