On Ext-indices of ring extensions |
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Authors: | Saeed Nasseh Yuji Yoshino |
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Institution: | a Department of Mathematics, Shahid Beheshti University, Tehran, Iran b Institute for Studies in Theoretical Physics and Mathematics, 19395-5746, Tehran, Iran c Department of Mathematics, Faculty of Science, Okayama University, 700-8530, Okayama, Japan |
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Abstract: | In this paper, we investigate the finiteness of Ext-indices for certain ring extensions. In this direction, we introduce some conjectures and discuss the relationships among them. We also prove these conjectures in some special cases. Furthermore, we prove that the trivial extension of an Artinian local ring by its residue class field is always of finite Ext-index, and prove a generalization of the Auslander-Reiten conjecture for this type of ring. |
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Keywords: | 13C10 13D07 16E30 |
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