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| Title | : | On representation of polynomial ring on a vector space via a linear transformation |
| Author | : |
Prof. Dr. Sri Wahyuni, S.U. (1) Prof. Dr.rer.nat. Indah Emilia Wijayanti, S.Si., M.Si. (2) NAIMAH HIJRIATI (3) |
| Date | : | 0 2017 |
| Keyword | : | representation of polynomial ring,vector space,linear transformation representation of polynomial ring,vector space,linear transformation |
| Abstract | : | A representation of a ring R is a ring homomorphism from R to the ring of all linear transformations from V to V (End F (V)). From the field F, we can form a polynomial ring F[X]. A representation of F[X] is a ring homomorphism phiv: F[X] ? End F (V ) via linear transformation T : V ? V with phiv(f(X)) = f(T) for all f(X) ? F[X]. For general ring representation ?: R ? End F (V), we have notions of admissibility submodule, and completely reducible and simple admissible submodule. In this paper, we will show that admissible submodules of V are invariant under T, and a representation of F[X] is completely reducible. |
| Group of Knowledge | : | Matematika |
| Original Language | : | English |
| Level | : | Internasional |
| Status | : |
Published
|