MATRIX RINGS OF INVARIANT SUBSPACES

Abstract

Consider a set V of R-submodules of R _n, R a commutative ring. We provide a sufficient condition on V such that the ring of all R-endomorphisms of R _n, which leave every R-submodule in V invariant, is a structural matrix ring. We also obtain results suggesting strongly that the mentioned condition is necessary too in case R is a field.