Minimal Monomial Reductions and the Reduced Fiber Ring of an Extremal Ideal
| dc.creator | Singla, Pooja | |
| dc.date | 2005-12-20 | |
| dc.date.accessioned | 2026-07-07T06:55:32Z | |
| dc.date.available | 2026-07-07T06:55:32Z | |
| dc.description | Let $I$ be a monomial ideal in a polynomial ring $A=K[x_1,...,x_n]$. We call a monomial ideal $J$ to be a minimal monomial reduction ideal of $I$ if there exists no proper monomial ideal $L \subset J$ such that $L$ is a reduction ideal of $I$. We prove that there exists a unique minimal monomial reduction ideal $J$ of $I$ and we show that the maximum degree of a monomial generator of $J$ determines the slope $p$ of the linear function $\reg(I^t)=pt+c$ for $t\gg 0$. We determine the structure of the reduced fiber ring $\mathcal{F}(J)_{\red}$ of $J$ and show that $\mathcal{F}(J)_{\red}$ is isomorphic to the inverse limit of an inverse system of semigroup rings determined by convex geometric properties of $J$. | |
| dc.identifier | https://arxiv.org/abs/math/0512456 | |
| dc.identifier | http://arxiv.org/abs/math/0512456 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106311 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13A30;13C99 | |
| dc.title | Minimal Monomial Reductions and the Reduced Fiber Ring of an Extremal Ideal | |
| dc.type | text |