A note on the regularity of products
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2010
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| _version_ | 1866912189939449856 |
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| author | Hassanzadeh, Seyed Hamid Yassemi, Siamak |
| author_facet | Hassanzadeh, Seyed Hamid Yassemi, Siamak |
| contents | Let $S={\Bbb K}[x_1,\dots,x_n]$ denote a polynomial ring over a field $\Bbb K$. Given a monomial ideal $I$ and a finitely generated multigraded $M$ over $S$, we follow Herzog's method to construct a multigraded free $S$-resolution of $M/IM$ by using multigraded $S$-free resolutions of $S/I$ and $M$. The complex constructed in this paper is used to prove the inequality $\Reg(IM)\leq \Reg(I)+\Reg(M)$ for a large class of ideals and modules. In the case where $M$ is an ideal, under one relative condition on the generators which specially does not involve the dimensions, the inequality $\Reg(IM)\leq \Reg(I)+\Reg(M)$ is proven. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1005_4638 |
| institution | arXiv |
| publishDate | 2010 |
| record_format | arxiv |
| spellingShingle | A note on the regularity of products Hassanzadeh, Seyed Hamid Yassemi, Siamak Commutative Algebra Let $S={\Bbb K}[x_1,\dots,x_n]$ denote a polynomial ring over a field $\Bbb K$. Given a monomial ideal $I$ and a finitely generated multigraded $M$ over $S$, we follow Herzog's method to construct a multigraded free $S$-resolution of $M/IM$ by using multigraded $S$-free resolutions of $S/I$ and $M$. The complex constructed in this paper is used to prove the inequality $\Reg(IM)\leq \Reg(I)+\Reg(M)$ for a large class of ideals and modules. In the case where $M$ is an ideal, under one relative condition on the generators which specially does not involve the dimensions, the inequality $\Reg(IM)\leq \Reg(I)+\Reg(M)$ is proven. |
| title | A note on the regularity of products |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/1005.4638 |