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 serial ring (generalized uniserial in the terminology of Nakayama) is one whose left and
right free modules are direct sums of modules with unique finite composition series …

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 …

A module is serial if its submodules are linearly ordered with respect to inclusion. A ring R is
called left serial if RR is a direct sum of serial modules, and R is called serial if it is both left …

Rings Whose Modules Are {oplus}-Supplemented Page 1 Ž . Journal of Algebra 218, 470487
1999 Article ID jabr.1998.7830, available online at http:rrwww.idealibrary.com on Rings Whose …

In the study of hereditary Noetherian rings, it is clear that hereditary Noetherian prime rings
will play a central role (see, for example,[12]). Here we study the (two-sided) ideals of an …

A Dedekind prim r&g [18] is an hereditary Koetherian prime ring'which is a maximal order in
its quotient ring, or equivalently [5] an hereditary Koetherian prime ring with no proper …

A module M is called a serial module if the family of its submodules is linearly ordered under
inclusion. A ring R is said to be serial if RR as well as RR are finite direct sums of serial …

Abstract A right R-module C is proper cyclic in case R→ C→ 0 is exact but 0→ R→ C→ 0 is
not. A ring R is a ring PCI ring if every proper cyclic right R-module is injective (PC⇒ I ring”) …

Throughout this paper R will be a commutative ring with identity, usually an integral domain.
Bourbaki [8] has defined an integral domain R to be pseudo-principal if every divisorial ideal …