Serial module

In abstract algebra, a uniserial module M is a module over a ring R, whose submodules are totally ordered by inclusion. This means simply that for any two submodules N₁ and N₂ of M, either or . A module is called a serial module if it is a direct sum of uniserial modules. A ring R is called a right uniserial ring if it is uniserial as a right module over itself, and likewise called a right serial ring if it is a right serial module over itself. Left uniserial and left serial rings are defined in an analogous way, and are in general distinct from their right counterparts.