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 K\”othe’s conjecture,
(iii) \Nil(R) is closed under the operation x\krogec 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.



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Šter, Janez