在抽象代数之分支环理论中，一个环 R 的雅各布森根（Jacobson radical）是 R 的一个理想，包含在某种意义上“与零接近”的那些元素。

雅各布森根记做 J(R) 可用如下等价的方式定义：

注意，最后一个性质不意味着 R 中使 1-x 可逆的任何元素 x 都是 J(R) 的一个元素。

另外，如果 R 不可交换，则 J(R) 不必等于 R 中所有双边极大理想之交。

雅各布森根也能对没有恒同元素（或说单位）的环定义。参见 I. N. Herstein 所着《Noncommutative Rings》。

In mathematics, more specifically ring theory, a branch of abstract algebra, the Jacobson radical of a ring R is the ideal consisting of those elements in R that annihilate all simple right R-modules. It happens that substituting "left" in place of "right" in the definition yields the same ideal, and so the notion is left-right symmetric. The Jacobson radical of a ring is frequently denoted by J(R) or rad(R); however to avoid confusion with other radicals of rings, the former notation will be preferred in this article. The Jacobson radical is named after Nathan Jacobson, who was the first to study it for arbitrary rings in (Jacobson 1945).