Modules in Which Every Fully Invariant Submodule is Essential in a Direct Summand

By G. Birkenmeier, Bruno J. Müller, Tariq S. Rizvi. 2002

129 citations recorded by the source corpus.

Subfields: Algebra and Number Theory

View Paper: https://www.semanticscholar.org/paper/86bc0764bb55565617e418d405e75cff027fb7b5

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In Algebra and Number Theory

1. C. Roman
2. S. Tariq Rizvi
3. G. Birkenmeier
4. J. Park
5. A. Tercan
6. E. Akalan
7. Gangyong Lee

Citations in the corpus

• Goldie Extending Modules (2009, background): “( 2002 ), a module is said to be FI-extending if every fully invariant submodule is essential in a direct summand.”
• Baer and Quasi-Baer Modules (2004, methodology): “A large class of modules and rings are FI-extending, but not necessarily extending (for example, direct sums of uniform modules, ring of upper-triangular matrices over Z; see Birkenmeier et al., 2002a).”
• Generalized Triangular Matrix Rings and the Fully Invariant Extending Property (2002, background): “In [1, 4] and [5], the FI-extending property was introduced and investigated.”
• MODULES WITH FULLY INVARIANT SUBMODULES ESSENTIAL IN FULLY INVARIANT SUMMANDS (2002, background): “From (1), (3) and (24), this example has ZðRRÞ 61⁄4 0, ZðRRÞ 1⁄4 0, R is strongly 1846 BIRKENMEIER, PARK, AND RIZVI”