Semisimple Algebra - Pure Mathematics - Algebra Dictionary Definition An associative algebra whose (left/right) modules are completely reducible; in the finite-dimensional case equivalently an algebra with zero Jacobson radical, admitting a decomposition as a finite direct product of simple algebras.
Semisimple Algebra - Pure Mathematics - Algebra Dictionary Definition An associative algebra whose (left/right) modules are completely reducible; in the finite-dimensional case equivalently an algebra with zero Jacobson radical, admitting a decomposition as a finite direct product of simple algebras.