In mathematics, the term socle has several related meanings.
The socle is a direct product of minimal normal subgroups.
Considering R as a right R-module, soc(RR) is defined, and considering R as a left R-module, soc(RR) is defined.
In the context of Lie algebras, a socle of a symmetric Lie algebra is the eigenspace of its structural automorphism that corresponds to the eigenvalue −1.
(A symmetric Lie algebra decomposes into the direct sum of its socle and cosocle.