Structural matrix algebras and their lattices of invariant subspaces Original Research Article

A structural matrix algebra image of n × n matrices over a field F has a distributive lattice Latimage of invariant subspaces subset of or equal toFn. This and related known results are reproven here in a fresh way. Further we investigate what happens when image still operates on Fn but is isomorphic to a structural matrix algebra of m × m matrices (m ≠ n). Then m < n and Latimage contains a certain distributive sublattice but needs not itself be distributive. If m is not too small, a shadow of distributivity is retained in the form of 2-distributivity and subdirect reducibility of Latimage.