1 results
A characterization of potent rings
-
- Journal:
- Glasgow Mathematical Journal / Volume 65 / Issue 2 / May 2023
- Published online by Cambridge University Press:
- 02 November 2022, pp. 324-327
- Print publication:
- May 2023
-
- Article
-
- You have access
- Open access
- HTML
- Export citation
-
An associative ring R is called potent provided that for every
$x\in R$, there is an integer 
$n(x)>1$ such that 
$x^{n(x)}=x$. A celebrated result of N. Jacobson is that every potent ring is commutative. In this note, we show that a ring R is potent if and only if every nonzero subring S of R contains a nonzero idempotent. We use this result to give a generalization of a recent result of Anderson and Danchev for reduced rings, which in turn generalizes Jacobson’s theorem.
