POLYMATROIDAL IDEALS AND LINEAR RESOLUTION | ||
| Journal of Algebraic Systems | ||
| دوره 11، شماره 2، فروردین 2024، صفحه 147-153 اصل مقاله (122.14 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2022.11950.1610 | ||
| نویسنده | ||
| Somayeh Bandari* | ||
| Department of Mathematics, Buein Zahra Technical University, Buein Zahra, Qazvin, Iran. | ||
| چکیده | ||
| Let $S=K[x_1,\ldots,x_n]$ be a polynomial ring over a field $K$ and $I\subset S$ be a monomial ideal with a linear resolution. Let $\frak{m}=(x_1,\ldots,x_n)$ be the unique homogeneous maximal ideal and $I\frak{m}$ be a polymatroidal ideal. We prove that if either $I\frak{m}$ is polymatroidal with strong exchange property, or $I$ is a monomial ideal in at most 4 variables, then $I$ is polymatroidal. We also show that the first homological shift ideal of polymatroidal ideal is again polymatroidal. | ||
| کلیدواژهها | ||
| polymatroidal ideals؛ monomial localization؛ linear quotients؛ linear resolution؛ homological shift ideal | ||
| مراجع | ||
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