STRUCTURE OF VIRTUALLY SEMISIMPLE RING
Semisimple module is one of modules class that have important role in module theory and its application. One of the most important result in this topic is Wedderburn-Artin Theorem. In this book, we give natural generalization of semisimple modules and generalization of Wedderburn-Artin Theorem. T...
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| Main Author: | |
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/35467 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Semisimple module is one of modules class that have important role in
module theory and its application. One of the most important result in this topic
is Wedderburn-Artin Theorem. In this book, we give natural generalization of
semisimple modules and generalization of Wedderburn-Artin Theorem. Then, we
investigate modules RM that every submodules of M are direct summand of M,
then we called that module as virtually semisimple module. We say that module
RM is completely virtually semisimple module if every submodules of M are
virtually semisimple R-modules. After that, a ring R called (completely) virtually
semisimple ring if left R-module R is a (completely) virtually semisimple module.
Generalized Wedderburn-Artin Theorem say that R is completely virtually semisimple
ring if and only if R =
Qk
i=1Mni(Di) where Di principal left ideal domain
for every i = 1; : : : ; k, and k; n1; : : : ; nk 2 N. |
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