Socle - Mathematics & Logic - Pure Mathematics Dictionary Definition The socle of a module or ring is the sum of all its minimal nonzero submodules (or minimal ideals); it is the largest semisimple subobject contained in the module and equals the direct sum of all simple submodules.
Socle - Mathematics & Logic - Pure Mathematics Dictionary Definition The socle of a module or ring is the sum of all its minimal nonzero submodules (or minimal ideals); it is the largest semisimple subobject contained in the module and equals the direct sum of all simple submodules.