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arXiv · 1510.07523

Rings in which nilpotents form a subring

Janez Šter
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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.

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Janez Šter. 2015-10-26. Rings in which nilpotents form a subring. https://arxiv.org/abs/1510.07523

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