On the Non-Cohen–Macaulayness of Certain Factorial Closures
| Autor: | Peter Schenzel, Mariam Imtiaz |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Communications in Algebra. 41:3397-3413 |
| ISSN: | 1532-4125 0092-7872 |
| Popis: | Let R = K[x, y, z] denote the polynomial ring in three variables over an arbitrary field K. We study the factorial closure B(E) of certain R-modules E of projective dimension 1, called monomial modules. By an explicit computation, we derive an example of an algebra which is a factorial non-Cohen–Macaulay ring if the characteristic of the basic field char k is two. To this end, we study examples of monomial modules E such that the factorial closure B(E) is generated by elements of degree at most 3 over the symmetric algebra Sym(E). In order to do that it will be necessary to understand—at least partially—the third component B(E)3 of the factorial closure. This work continues the investigations of Imtiaz and Schenzel [7] were the case of monomial modules was described such that the factorial closure B(E) is generated in degrees at most two. |
| Databáze: | OpenAIRE |
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