Minimal polynomials and characteristic polynomials over rings

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Let R be a commutative ring with 1, and M be a free module of a finite rank over R. is the endomorphism ring of M over R, s is an element in and the matrix of s diagonalizable. Our purpose is to investigate the relationship between the characteristic polynomial of s and the minimal polynomial of s. If R is an integral domain, then we shall show that is uniquely determined as a monic polynomial dividing Also, the difference between the two sets of zeros of and respectively, is only the multiplicity of their roots. If R is not an integral domain, then we shall construct s such that is not necessarily monic nor divides

identifier:JOS-09725555-2001

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