… Let RN be a left R-module and let B = End RM be its endomorphism ring. When … , Gl and
G2, which exist between the lattice, L, of submodules of M and the lattices, L, or L,, of right or left …

… by elements of its lattice … show that the endomorphism ring of a module which is the direct
sum of more than three isomorphic submodules is determined up to isomorphism by its lattice …

… lattice, L(V), of submodules of V and the lattices L(B.) and L(3) of right and left ideals of B, and
consequently lattice … of the “closed” submodules of V and the lattices J& and dz of right and …

… , over rings R not necessarily containing a 1. We denote the lattice of submodules of RM by
… understand that E is a lattice isomorphism between the lattices of submodules of RM and SN. …

… ring. In doing so we extend the corresponding well-known theorems for rings (employing them
in the process) to endomorphism rings… complete complemented lattice and ^(¡¡M) is lattice …

… lattices and the consequences of the existence of a lattice decomposition. In sections three
and four we study distributive submodules … this endomorphism stabilizes every submodule. In …

… The mapping S ~-~ S' is a lattice anti-isomorphism of the lattice of closed submodules of A …
even if A has a finite basis there may exist proper submodules B of A* with the property that (x, …

… R-module and E = End,(P) be its endomorphism ring. If P is … 2.3 will relate the R-submodules
of P to equivalence classes of … a lattice isomorphism between the lattice of Rsubmodules of …

… M is a right R-module with endomorphism ring … a submodule of the canonical left S-moQule
M. Thus, we may refer to S-submodules of M which are not necessarily R-submodules. An R-…

… of the rings that can be realized as endomorphism rings of artinian modules, and serial rings
… Hence a module M is uniserial if and only if the lattice £(M) of its submodules is linearly …