Orthogonal Dimensions and Ring Extensions

Abstract

Let , ℬ be classes of modules, we introduce and characterize orthogonal dimensions of modules and rings by the orthogonal classes of modules  ^⊥, ^⊥ ℬ, and  ^T . For an almost excellent extension S ≥ R, we give the criteria to test some identities of orthogonal dimensions of modules and rings. As corollaries, some known results are obtained or extended.

Keywords:

• Orthogonal dimension
• Ring extension

Mathematics Subject Classification:

• 16D10
• 16E40

ACKNOWLEDGMENTS

The author wishes to thank Professors Wenting Tong and Weimin Xue for many valuable suggestions and helpful communications. It is the author's pleasure to thank the referee for his interesting ideals on this further research. This research is supported by the Natural Science Foundation of China (No. A0324656) the Scientific Research Foundation of Fujian Province (No. JA05212) and the Fumiao Foundation of Fujian Normal University (No. F029).