Construction of Modules with Finite Homological Dimensions |
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Authors: | Oana Veliche |
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Institution: | Department of Mathematics, Purdue University, West Lafayette, Indiana, 47907, f1 |
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Abstract: | A new homological dimension, called G*-dimension, is defined for every finitely generated module M over a local noetherian ring R. It is modeled on the CI-dimension of Avramov, Gasharov, and Peeva and has parallel properties. In particular, a ring R is Gorenstein if and only if every finitely generated R-module has finite G*-dimension. The G*-dimension lies between the CI-dimension and the G-dimension of Auslander and Bridger. This relation belongs to a longer sequence of inequalities, where a strict inequality in any place implies equalities to its right and left. Over general local rings, we construct classes of modules that show that a strict inequality can occur at almost every place in the sequence. |
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