论文标题
纯粹的理想和痕迹理想的一些结果
Some results on pure ideals and trace ideals of projective modules
论文作者
论文摘要
令$ r $为单位元素的交换戒指。结果表明，$ r $中的理想$ i $是纯粹的，并且仅当in i $中的所有$ f \ in ann $（f）+i = r $。如果$ j $是投影$ r $ -module $ m $的痕迹，我们证明$ j $是由$ m $和$ m $和$ jm = m $的``坐标''生成的。这些导致了一些新的结果和其他证明，以获得一些已知结果。
Let $R$ be a commutative ring with the unit element. It is shown that an ideal $I$ in $R$ is pure if and only if Ann$(f)+I=R$ for all $f\in I$. If $J$ is the trace of a projective $R$-module $M$, we prove that $J$ is generated by the ``coordinates" of $M$ and $JM = M$. These lead to a few new results and alternative proofs for some known results.
