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Arithmetical Rank of Squarefree Monomial Ideals Generated by Five Elements or with Arithmetic Degree Four |
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| Authors: | Kyouko Kimura Giancarlo Rinaldo Naoki Terai |
| Affiliation: | 1. Department of Mathematics, Faculty of Science , Shizuoka University , Suruga-ku , Shizuoka , Japan skkimur@ipc.shizuoka.ac.jp;3. Dipartimento di Matematica , Universita’ di Messina , Messina , Italy;4. Department of Mathematics, Faculty of Culture and Education , Saga University , Saga , Japan |
| Abstract: | Let I be a squarefree monomial ideal of a polynomial ring S. In this article, we prove that the arithmetical rank of I is equal to the projective dimension of S/I when one of the following conditions is satisfied: (1) μ(I) ≤5; (2) arithdeg I ≤ 4. |
| Keywords: | Arithmetical rank Monomial ideal Projective dimension |