It is classically known that idempotents lift modulo nil one-sided ideals. So it is natural to ask if the same is true for potent elements. Although we answer this question in negative, we prove that the answer is positive in several special cases. For instance, the answer is positive in rings with finite characteristic. Let I be a nil one sided ideal of R and $x\in R$ is such that $x^{n+1}-x\in I$ for some positive integer n. We prove that if n is a unit in R, then there exists an element $p\in R$ with $p^{n+1}=p$ such that $x-p\in I$. By taking $n=1$, the result that idempotents lift modulo nil one sided ideals is retrieved. For a nil ideal I of an abelian ring R, we prove that potent elements lift modulo I precisely when torsion units or periodic elements lift modulo I. It follows that torsion units or periodic elements may also not lift modulo nil ideals. We prove that torsion units, potent elements and periodic elements lift modulo every nil ideal of a π- regular ring.

众所周知，幂等数是无模单边理想。因此很自然地要问对有效元素是否同样如此。尽管我们以否定的方式回答这个问题，但我们证明在某些特殊情况下答案是肯定的。例如，在具有有限特征的环中答案是肯定的。让我成为一个零一个片面的理想[R和$X\in \mathrm{[R}$ 就是这样 $X^{ñ+\mathrm{1个}}-X\in \mathrm{一世}$对于一些正整数n。我们证明如果n是R中的一个单位，则存在一个元素$p\in \mathrm{[R}$ 和 $p^{ñ+\mathrm{1个}}=p$ 这样 $X-p\in \mathrm{一世}$。通过采取$ñ=\mathrm{1个}$，求出幂等式以单边理想取模的结果。对于阿贝尔环R的零理想I，我们证明了当扭转单位或周期元素提升模I时，有效元素的模I精确地提升。随之而来的是，扭力单元或周期元素也可能无法达到模理想值。我们证明了扭转单位，有效元素和周期元素对π-正则环的每零个理想点取模。