Modules in Which Every Fully Invariant Submodule is Essential in a Direct Summand
2002; Taylor & Francis; Volume: 30; Issue: 3 Linguagem: Inglês
10.1080/00927870209342387
ISSN1532-4125
AutoresGary F. Birkenmeier, Bruno J. Müller, S. Tariq Rizvi,
Tópico(s)Commutative Algebra and Its Applications
ResumoAbstract A module M is called extending if every submodule of M is essential in a direct summand. We call a module FI-extending if every fully invariant submodule is essential in a direct summand. Initially we develop basic properties in the general module setting. For example, in contrast to extending modules, a direct sum of FI-extending modules is FI-extending. Later we largely focus on the specific case when a ring is FI-extending (considered as a module over itself). Again, unlike the extending property, the FI-extending property is shown to carry over to matrix rings. Several results on ring direct decompositions of FI-extending rings are obtained, including a proper generalization of a result of C. Faith on the splitting-off of the maximal regular ideal in a continuous ring.
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