SEMIMODUL PRIMA PENUH
The dissertation’s area is about a fully prime semimodules. At the beginning of its development, the study of the concept of prime starts from the structure of ideal in the ring. The prime ideals are introduced by Dedekind. It is extended by Goldie to the ring’s structure and then by Feller and S...
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| Format: | Dissertations |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/69869 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | The dissertation’s area is about a fully prime semimodules. At the beginning of its
development, the study of the concept of prime starts from the structure of ideal in
the ring. The prime ideals are introduced by Dedekind. It is extended by Goldie
to the ring’s structure and then by Feller and Swokowski to the module’s structure.
The fully prime concept is a development of the prime concept. Since semimodules
are a weaker structure of modules, the results obtained in fully prime modules can
be applied to semimodules. In addition, in this research, we will try to characterize
fully prime semimodules based on their subsemimodules and ideals in their
semiring.
This dissertation is an extension of the results obtained in fully prime modules. In
research by Behboodi et al. obtained equivalence of fully prime modules related
to homogeneous semisimple modules, prime cyclic submodules, semiprime cyclic
submodules, maximal submodules, semisimple modules, descending chain conditions
in finitely generated submodules, and the Socle from their modules. Not
all equivalence in fully prime modules satisfies to fully prime semimodules, so
some conditions are required in semimodules. This dissertation also examines the
relationship between fully prime semimodules and fully prime semirings. |
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