论文标题
有限尺寸多项式模块的降低的子模块
Reduced submodules of finite dimensional polynomial modules
论文作者
论文摘要
令$ k $为具有特征零的字段，$ r $为环$ k [x_1，\ cdots，x_n] $，而$ i $是$ r $的单一理想。当将Artinian本地代数$ r/i $视为$ r $ -MODULE $ m $时。我们表明，最大的$ m $减少sodule与$ m $的socle和$ k $ -submodule of $ m $ of $ m $，这是所有与$ m $相关的Young图的外部角元素产生的。根据链球条逆系统给出了不同减少模块的解释。进一步表明，这些减少的子模块是无扭转型类中模块的示例，以及它们的双重模块。成排成熟的模块，关于Matlis二元性和扭转理论的对称性。最后，我们证明此处描述的任何$ r $ -Module $ m $都可以满足激进公式。
Let $k$ be a field with characteristic zero, $R$ be the ring $k[x_1, \cdots, x_n]$ and $I$ be a monomial ideal of $R$. We study the Artinian local algebra $R/I$ when considered as an $R$-module $M$. We show that the largest reduced submodule of $M$ coincides with both the socle of $M$ and the $k$-submodule of $M$ generated by all outside corner elements of the Young diagram associated with $M$. Interpretations of different reduced modules is given in terms of Macaulay inverse systems. It is further shown that these reduced submodules are examples of modules in a torsion-torsionfree class, together with their duals; coreduced modules, exhibit symmetries in regard to Matlis duality and torsion theories. Lastly, we show that any $R$-module $M$ of the kind described here satisfies the radical formula.
