CHARACTERIZATION OF AUTOMORPHISM-INVARIANT MODULE BY ITS INJECTIVITY
Let M be a module over ring R. An Injective hull of M, denoted by E(M), is an injective module which contain M as its essential submodule. If M is invariant under any automorphism of E(M), then M is called an automorphism- invariant module. Direct summand of an automorphism-invariant module is auto...
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| Format: | Theses |
| Language: | Indonesia |
| Subjects: | |
| Online Access: | https://digilib.itb.ac.id/gdl/view/34872 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Let M be a module over ring R. An Injective hull of M, denoted by E(M), is an injective module which contain M as its essential submodule. If M is invariant under any automorphism of E(M), then M is called an automorphism-
invariant module. Direct summand of an automorphism-invariant module is automorphism-invariant, and if the direct sum M1 o M2 is automorphism-invariant then M1 dan M2 are relatively injective. The sufficient and neces-
sary condition for a module M to be automorphism-invariant is every isomor-phism between two essential submodules of M extend to an endomorphism of M. This gives a result that every pseudo-injective module is automorphism-invariant. In this thesis showed that the module M is automorphism-invariant if and only if M pseudo-injective. |
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