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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 domain]]s, and matrix rings over a field.

See also: [[Baer semi-group]].

====References====
* Tsit-Yuen Lam, "Lectures on Modules and Rings" Graduate Texts in Mathematics '''189''' Springer (2012) {{ISBN|1461205255}} {{ZBL|0911.16001}}

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