Baer ring

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A Baer ring is a ring $R$ in which every left annihilator is generated by an idempotent $e$. The analogous definition in terms of right annihilators is equivalent . A Baer ring is necessarily a left and a right Rickart ring.

Examples of Baer rings include integral domains, and matrix rings over a field.

See also: Baer semi-group.


  • Tsit-Yuen Lam, "Lectures on Modules and Rings" Graduate Texts in Mathematics 189 Springer (2012) ISBN 1461205255 Zbl 0911.16001
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