RINGS WHOSE MODULES ARE DIRECT SUMS OF EXTENDING MODULES


Er N. F.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, cilt.137, ss.2265-2271, 2009 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 137 Konu: 7
  • Basım Tarihi: 2009
  • Doi Numarası: 10.1090/s0002-9939-09-09807-4
  • Dergi Adı: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Sayfa Sayıları: ss.2265-2271

Özet

We prove that for a ring R, the following are equivalent: (i) Every right R-module is a direct sum of extending modules, and (ii) R has finite type and right colocal type (i.e., every indecomposable right R-module has simple socle). Thus, in this case, R is two-sided Artinian and right serial, and every right R-module is a direct sum of finitely generated uniform modules. This property of a ring is not left-right symmetric. A consequence is the following: R is Artinian serial if and only if every R-module is a direct sum of extending modules if and only if R is left serial with every right R-module a direct sum of extending modules.