On representation of polynomial ring on a vector space via a linear transformation
Penulis/Author
Prof. Dr. Sri Wahyuni, S.U. (1); Prof. Dr.rer.nat. Indah Emilia Wijayanti, S.Si., M.Si. (2); NAIMAH HIJRIATI (3)
Tanggal/Date
2017
Kata Kunci/Keyword
Abstrak/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.
