carpathian_2016_32_2_251_258_abstractcarpathian_2016_32_2_251_258Let 
be a ring with the set of nilpotents 
. We prove that the following are equivalent:
(i) is additively closed,
(ii) is multiplicatively closed and satisfies K\”othe’s conjecture,
(iii) is closed under the operation 
,
(iv) is a subring of .
Some applications and examples of rings with this property are given, with
an emphasis on certain classes of exchange and clean rings.
| Author(s) | Šter, Janez |
|---|
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