Note on Morita Equivalence in Ring Extensions

Abstract

It seems that Morita invariance judges of the importance of classes of ring extensions concerned. Miyashita introduced the notion of Morita equivalence in ring extensions, and he showed that the classes of G-Galois extensions and Frobenius extensions are Morita invariant. After that, Ikehata showed that the classes of separable extensions, Hirata separable extensions, symmetric extensions, and QF-extensions are Morita invariant. In this article, we shall prove that the classes of several extensions are Morita invariant. Further, we will give an example of the class of ring extensions which is not Morita invariant.

Key Words:

• Morita equivalence
• Ring extension

2010 Mathematics Subject Classification:

• 16D90
• 16S70

ACKNOWLEDGMENTS

The author wishes to thank Professor S. Ikehata with whose guidance and encouragement this work was done. The author also would like to thank the referee for his valuable suggestions.