Rings in which nilpotents form a subring
Rings and Algebras
2016-07-11 v1
Abstract
Let R be a ring with the set of nilpotents Nil(R). We prove that the following are equivalent: (i) Nil(R) is additively closed, (ii) Nil(R) is multiplicatively closed and R satisfies Koethe's conjecture, (iii) Nil(R) is closed under the operation x\circ y=x+y-xy, (iv) Nil(R) is a subring of R. Some applications and examples of rings with this property are given, with an emphasis on certain classes of exchange and clean rings.
Cite
@article{arxiv.1510.07523,
title = {Rings in which nilpotents form a subring},
author = {Janez Šter},
journal= {arXiv preprint arXiv:1510.07523},
year = {2016}
}