AI 中文总结
研究域上多项式环中由至少两个二次二项式极小生成，满足素理想、科恩 - 麦考利且有线性分解条件的理想\(I\)，探讨其是否等于变量\((2×n)\)矩阵的\(2 -\)子式理想。
AI 中文摘要
设\(I\)是域\(K\)上多项式环\(S\)的一个理想，由至少两个二次二项式极小生成。假设：(i)\(I\)是素理想；(ii)\(S/I\)是科恩 - 麦考利的；(iii)\(I\)具有线性分解。主要研究\(I\)是否等于变量的\((2×n)\)矩阵的\(2 -\)子式理想。
英文摘要
Let $I$ be an ideal of a polynomial ring $S$ over a field $K$ for which $I$ is minimally generated by at least two quadratic binomials. Suppose that (i) $I$ is prime, (ii) $S/I$ is Cohen--Macaulay and (iii) $I$ has linear resolution. The question whether $I$ is equal to the ideal of $2$-minors of a $(2 \times n)$-matrix of variables is mainly studied.
