ACADSTAFF UGM
| Title | : | On representation of a ring on a free modules over a commutative ring with identity |
| Author | : |
NAIMAH HIJRIATI (1) Prof. Dr. Sri Wahyuni, S.U. (2) Prof. Dr.rer.nat. Indah Emilia Wijayanti, S.Si., M.Si. (3) |
| Date | : | 0 2016 |
| Keyword | : | --,On representation of a ring on a free modules over a commutative ring with identity --,On representation of a ring on a free modules over a commutative ring with identity |
| Abstract | : | Let R be a commutative ring with identity and M be a free R-module then we always have a representation of R, that is homomorphism ring μ: R → EndR(M), with μ(r) := μr : M → M and μr(m) = rm for all r ∈ R and for all m ∈ M. In this paper, we will present some properties of representations of ring R on R-module, based on some notions in representation of R on vector space, such as admissible submodule, equivalence of two representations, decomposable representation and completely reducible representation. It will be shown that if M, N are two free R-modules then two representations μ: R→ EndR(M) and φ: R → EndR(N) are equivalent if and only if there is a module isomorphism T : M → N. If R is a principle ideal domain(PID), then it will be shown that every submodule of M is an admissible submodule of M, every representation of ring R on a free R-module is decomposable, and a representation of R on M is completely reducible if and only if M is semisimple. |
| Group of Knowledge | : | Matematika |
| Level | : | Internasional |
| Status | : |
Published
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| No | Title | Action |
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| 1 |
Sertifikat-AMC-Naimah.pdf
Document Type : Artikel dan Sertifikat/Bukti Kehadiran/Pasport (jika tidak ada sertifikat)
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| 2 |
On representation of a ring on a free module over a commutative ring with identity (2).pdf
Document Type : Cek Similarity
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| 3 |
Scopus - Document details - On representation of polynomial ring on a vector space via a linear transformation _ Signed in.pdf
Document Type : Dokumen Pendukung Karya Ilmiah (Hibah, Publikasi, Penelitian, Pengabdian)
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| 4 |
On representation of a ring on a free modules over a commutative ring with identity.pdf
Document Type : [PAK] Full Dokumen
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| 5 |
On representation of a ring on a free modules over a commutative ring with identity.pdf
Document Type : [PAK] Full Dokumen
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| 6 |
prosiding_On representation of a ring on a free modules over a commutative ring with identity.pdf
Document Type : [PAK] Full Dokumen
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