saujs

Sakarya University Journal of Science

2147-835X

Sakarya University

10.16984/saufenbilder.420612

Mathematical Sciences

Matematik

Extending property on EC-Fully Submodules

Yaşar

Ramazan

HACETTEPE ÜNİVERSİTESİ Tercan

Adnan

12 01 2018

22 6 1799 1803 05 03 2018 06 26 2018

1997

Sakarya University Journal of Science

Thereare several generalizations of -modulesin literature. One of the generalization is based on fully invariantsubmodules. Recall that amodule is called -extendingif every fully invariant submodule is essential in a direct summand. We call a module-extendingif every fully invariant submodule which contains essentially a cyclicsubmodule is essential in a direct summand. Initially we obtain basicproperties in the general module setting. For example, a direct sum of -extendingmodules is -extending.Again, like the -extendingproperty, the -extendingproperty is shown to carry over to matrix rings.

fully invariant ec-fully submodule FI-extending extending extending

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