HUBUNGAN RADICAL IDEAL NULL DAN IDEAL YANG DIBANGUN OLEH POLINOMIAL KARAKTERISTIK
Abstract
ABSTRACT
Cayley-Hamilton theorem states, if CA (x) is the characteristic polynomial of A, then CA (A) = 0. This theorem leads us to the null ideal concept of a matrix over a field. If A is a square matrix over field F, then the null ideal of A can be constructed by the characteristic polynomial. This study discusses the ideal null of square matrix over a commutative ring, then also discussed radical relationship with the ideal generated by the characteristic polynomial. This discussion begins with determining the necessary and sufficient condition of a polynomial are in null ideal.
Kata Kunci : Cayley-Hamilton Theorem, Communitative Ring, Characteristic Polynomial, Null Ideal.
Cayley-Hamilton theorem states, if CA (x) is the characteristic polynomial of A, then CA (A) = 0. This theorem leads us to the null ideal concept of a matrix over a field. If A is a square matrix over field F, then the null ideal of A can be constructed by the characteristic polynomial. This study discusses the ideal null of square matrix over a commutative ring, then also discussed radical relationship with the ideal generated by the characteristic polynomial. This discussion begins with determining the necessary and sufficient condition of a polynomial are in null ideal.
Kata Kunci : Cayley-Hamilton Theorem, Communitative Ring, Characteristic Polynomial, Null Ideal.
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