CHARACTERIZATION OF WEAKLY PRIME SUBMODULES
Let R be a commutative ring with non-zero identity and M be a unital module. An R-Module M is called multiplication if for each submodule of M is of the form IM for some ideal I of R. We say that I is a presentasion ideal of N. If M is a multiplication module then we can dene the product of two s...
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| Format: | Theses |
| Language: | Indonesia |
| Subjects: | |
| Online Access: | https://digilib.itb.ac.id/gdl/view/32156 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Let R be a commutative ring with non-zero identity and M be a unital module.
An R-Module M is called multiplication if for each submodule of M is of the
form IM for some ideal I of R. We say that I is a presentasion ideal of N. If M
is a multiplication module then we can dene the product of two submodules
by multiply every presentasion ideals of that submodules respectively, then
the result is multiplied by M. So that, the product of two elements can be
done in the same way, with assume the elements as cyclic submodules. If N
is submodule of M then (N : M) is dened by fr 2 RjrM Ng. If a proper
submodule N of M with rm 2 N (r 2 R;m 2 M) implies that either m 2 N
or r 2 (N : M), then N is called prime. Then concept of prime submodule was
extended to weakly prime submodule, with condition rm 6= 0. Every prime
submodule is weakly prime submodule, but the converse is not always true. In
this thesis, we will prove characterization of weakly prime submodules. |
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