Assassins和Torsion函子
Assassins and torsion functors
摘要：
设$R$是环，$\mathfrak{a}\subseteq R$是理想，$M$是$R$ -模。令$Γ_{\mathfrak{a}}$表示$\mathfrak{a}$ -扭函子。给出了$Γ_{\mathfrak{a}}(M)$的（弱）相伴素数是含有$\mathfrak{a}$的$M$的（弱）相伴素数和$M/Γ_{\mathfrak{a}}(M)$的（弱）相伴素数是不含$\mathfrak{a}$的$M$的（弱）相伴素数的条件.
英文摘要：
Let $R$ be a ring, let $\mathfrak{a}\subseteq R$ be an ideal, and let $M$ be an $R$-module. Let $Γ_{\mathfrak{a}}$ denote the $\mathfrak{a}$-torsion functor. Conditions are given for the (weakly) associated primes of $Γ_{\mathfrak{a}}(M)$ to be the (weakly) associated primes of $M$ containing $\mathfrak{a}$, and for the (weakly) associated primes of $M/Γ_{\mathfrak{a}}(M)$ to be the (weakly) associated primes of $M$ not containing $\mathfrak{a}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
