Volume 35 • Number 2 • 2012   • Weak Annihilator over Extension Rings Lunqun Ouyang and Gary F. Birkenmeier Abstract. Let $R$ be a ring and nil$(R)$ the set of all nilpotent elements of $R$. For a subset $X$ of a ring $R$, we define $N_R(X)=\{a\in R \mid xa\in$ nil$(R)$ for all $x\in X\},$ which is called the weak annihilator of $X$ in $R$. In this paper we mainly investigate the properties of the weak annihilator over extension rings. 2010 Mathematics Subject Classification: Primary: 13B25; Secondary: 16N60. Full text: PDF