Graded Version of Kato-Müller Theorem. Applications

Abstract

In this article, we prove that any graded Morita context between G -graded rings R and S , induces a graded equivalence between quotient categories of R -gr and S -gr. Under certain hypotheses (for example, when G is finite), there exists a commutative diagram connecting the graded and nongraded versions. For strongly graded rings, a Dade type equivalence for quotient categories is obtained. Finally, we prove a graded dual version of this theorem in the sense of Kato and Ohtake (1979).

Key Words:

• Graded equivalence
• Graded Morita context
• Graded ring
• Quotient category

Mathematics Subject Classification:

• 16W50
• 16D90
• 16S90

ACKNOWLEDGMENTS

The authors would like to thank the referee for the attentive reading of our manuscript and useful suggestions and corrections. Research partially supported by Spanish Project (BMF2002–02717) from MCT. Supported by the contract “Ramón y Cajal” administered by the University of Almería Spain.

Notes

^#Communicated by J. Gomez Pardo.