Rings with very few nilpotents

Received: 19.II.2016, Accepted: 10.I.2017

Abstract. We show that any indecomposable ring with only 3 nonzero nilpotent elements, pairwise not commuting, is isomorphic to the ring of $2\times 2$ matrices over the 2-element field. Rings with only one or two nonzero nilpotent elements are also investigated.
Keywords: indecomposable ring, nilpotent element, finite ring, nilpotent radical

Mathematics Subject Classification (2010): 16N40, 16U99, 16N60

Author

Grigore Călugăreanu, Department of Mathematics, Babeş-Bolyai University, 1 Kogălniceanu street, Cluj-Napoca, România