A module is uniserial if its submodules are linearly ordered by inclusion and it is serial if it is
a direct sum of uniserial submodules. This note is a study of rings whose finitely generated …

A module is uniserial in case its submodules are linearly ordered by inclusion. A ring R is left
(right) serial if it is a direct sum of uniserial left (right) R-modules. A ring R is serial if it is both …

A module is uniserial if its lattice of submodules is linearly ordered, and a ring R is left serial
if R is a direct sum of uniserial left ideals. The following problem is considered. Suppose the …

In 1-4] Nakayama proved that every module M over a generalized uniserial ring has a
decomposition M=~) M~ in which each term is A uniserial (ie, its submodules form a chain) …

In the second section we shall deal with more general rings than sl: rial rings defined by
Nakayama [lo]. He showed that if a ring R is a serial ring, 1; hen every finitely generated …

Nakayama, who called these rings generalized uniserial rings, proved [21, Theorem 171
that every finitely generated module over a serial ring is a direct sum of uniserial modules. In …

A module is called uniserial (or often simply serial) in case its lattice of submodules is a
chain. An artinian ring is called serial (or generalized uniserial) in case each of its …

The following conditions are shown to be equivalent: 1) ring A is generalized uniserial (not
necessarily artinian); 2) every finitely presented A module is semiserial; 3) A is semiperfect …

It is shown that if R is a commutative ring such that any R-module is a direct sum of
indecomposable modules, then R is an Artinian principal ideal ring (so that every module is …

This paper is a loosely connected collection of results on rings and modules. The first
section is concerned with quasi-injective modules of a ring. A module M is said to be quasi …