Displaying similar documents to “Rings without Nilpotent Elements”

Rings generalized by tripotents and nilpotents

Huanyin Chen, Marjan Sheibani, Nahid Ashrafi (2022)

Czechoslovak Mathematical Journal

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We present new characterizations of the rings for which every element is a sum of two tripotents and a nilpotent that commute. These extend the results of Z. L. Ying, M. T. Koşan, Y. Zhou (2016) and Y. Zhou (2018).

On Kolchin's theorem.

Israel N. Herstein (1986)

Revista Matemática Iberoamericana

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A well-known theorem due to Kolchin states that a semi-group G of unipotent matrices over a field F can be brought to a triangular form over the field F [4, Theorem H]. Recall that a matrix A is called unipotent if its only eigenvalue is 1, or, equivalently, if the matrix I - A is nilpotent. Many years ago I noticed that this result of Kolchin is an immediate consequence of a too-little known result due to Wedderburn [6]. This result of Wedderburn asserts that if B is a finite...