Schanuel's Lemma in P-Poor Modules
Modules are a generalization of the vector spaces of linear algebra in which the “scalars” are allowed to be from a ring with identity, rather than a field. In module theory there is a concept about projective module, i.e. a module over ring R in which it is projective module relative to all modules...
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| Format: | Article |
| Language: | English |
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Faculty of Science and Technology, UIN Sunan Ampel Surabaya
2019-10-01
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| Series: | Mantik: Jurnal Matematika |
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| Online Access: | http://jurnalsaintek.uinsby.ac.id/index.php/mantik/article/view/655 |
| Summary: | Modules are a generalization of the vector spaces of linear algebra in which the “scalars” are allowed to be from a ring with identity, rather than a field. In module theory there is a concept about projective module, i.e. a module over ring R in which it is projective module relative to all modules over ring R. Next, there is the fact that every module over ring R is projective module relative to all semisimple modules over ring R. If P is a module over ring R which it’s projective relative only to all semisimple modules over ring R, then P is called p-poor module. In the discussion of the projective module, there is a lemma associated with the equivalence of two modules K1 and K2 provided that there are two projective modules P1 and P2 such that is isomorphic to . That lemma is known as Schanuel’s lemma in projective modules. Because the p-poor module is a special case of the projective module, then in this paper will be discussed about Schanuel’s lemma in p-poor modules |
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| ISSN: | 2527-3159 2527-3167 |