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- W2020812794 abstract "A ring R is called NLI (rings whose nilpotent elements form a Lie ideal) if for each a ∈ N ( R ) and b ∈ R , ab − ba ∈ N ( R ). Clearly, NI rings are NLI . In this note, many properties of NLI rings are studied. The main results we obtain are the following: (1) NLI rings are directly finite and left min-abel; (2) If R is a NLI ring, then (a) R is a strongly regular ring if and only if R is a Von Neumann regular ring; (b) R is (weakly) exchange if and only if R is (weakly) clean; (c) R is a reduced ring if and only if R is a n -regular ring; (3) If R is a NLI left MC 2 ring whose singular simple left modules are Wnil -injective, then R is reduced." @default.
- W2020812794 created "2016-06-24" @default.
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- W2020812794 date "2014-06-01" @default.
- W2020812794 modified "2023-09-27" @default.
- W2020812794 title "Rings whose nilpotent elements form a Lie ideal" @default.
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- W2020812794 doi "https://doi.org/10.1556/sscmath.51.2014.2.1279" @default.
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