论文标题
完全关闭的$ \ Mathfrak {M} $ - 主要理想具有极好的决议
Integrally closed $\mathfrak{m}$-primary ideals have extremal resolutions
论文作者
论文摘要
我们表明，每一个全面关闭的$ \ mathfrak {m} $ - 主要的理想$ i $ $ $ $ $ $ $ $ $ $ $ $在noetherian本地环$（r，\ mathfrak {m}，k），k）$具有最大复杂性和曲率，即$ {\ rm cx} curv} _r（i）= {\ rm curv} _r（k）$。结果，我们根据复杂性，曲率和此类理想的完整相交维度来表征完整的相交局部环。已知有关投影，注射剂和戈伦斯坦尺寸的类似结果。但是，我们也提供了这些结果的简短证明。
We show that every integrally closed $\mathfrak{m}$-primary ideal $I$ in a commutative Noetherian local ring $(R,\mathfrak{m},k)$ has maximal complexity and curvature, i.e., $ {\rm cx}_R(I) = {\rm cx}_R(k) $ and $ {\rm curv}_R(I) = {\rm curv}_R(k) $. As a consequence, we characterize complete intersection local rings in terms of complexity, curvature and complete intersection dimension of such ideals. The analogous results on projective, injective and Gorenstein dimensions are known. However, we provide short proofs of these results as well.
