The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
Let be a ring and a right -module. is called -cofinitely supplemented if every submodule of with finitely generated has a supplement that is a direct summand of . In this paper various properties of the -cofinitely supplemented modules are given. It is shown that (1) Arbitrary direct sum of -cofinitely supplemented modules is -cofinitely supplemented. (2) A ring is semiperfect if and only if every free -module is -cofinitely supplemented. In addition, if has the summand sum...
The duals of -compact modules are briefly discussed.
We first propose a generalization of the notion of Mathieu subspaces of associative algebras
, which was introduced recently in [Zhao W., Generalizations of the image conjecture and the Mathieu conjecture, J. Pure Appl. Algebra, 2010, 214(7), 1200–1216] and [Zhao W., Mathieu subspaces of associative algebras], to
-modules
. The newly introduced notion in a certain sense also generalizes the notion of submodules. Related with this new notion, we also introduce the sets σ(N) and τ(N) of stable...
A module is called uniserial if it has totally ordered submodules in inclusion. We describe direct summands of for a uniserial module . It appears that any such a summand is isomorphic to a direct sum of copies of at most two uniserial modules.
Addendum to the author's article "Rings whose modules have maximal submodules", which appeared in Publicacions Matemàtiques 39, 1 (1995), 201-214.
Currently displaying 1 –
20 of
321