Geodesic
Cayley-Hamilton Theorem for Matrices over an Arbitrary Ring
Serdica Mathematical Journal, Tome 32 (2006) no. 2-3, pp. 269-276.

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For an n×n matrix A over an arbitrary unitary ring R, we obtain the following Cayley-Hamilton identity with right matrix coefficients: (λ0I+C0)+A(λ1I+C1)+… +An-1(λn-1I+Cn-1)+An (n!I+Cn) = 0, where λ0+λ1x+…+λn-1 xn-1+n!xn is the right characteristic polynomial of A in R[x], I ∈ Mn(R) is the identity matrix and the entries of the n×n matrices Ci, 0 ≤ i ≤ n are in [R,R]. If R is commutative, then C0 = C1 = … = Cn-1 = Cn = 0 and our identity gives the n! times scalar multiple of the classical Cayley-Hamilton identity for A.
Keywords: Commutator Subgroup [R,R] of a Ring R 
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     author = {Szigeti, Jeno},
     title = {Cayley-Hamilton {Theorem} for {Matrices} over an {Arbitrary} {Ring}},
     journal = {Serdica Mathematical Journal},
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     year = {2006},
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Szigeti, Jeno. Cayley-Hamilton Theorem for Matrices over an Arbitrary Ring. Serdica Mathematical Journal, Tome 32 (2006) no. 2-3, pp. 269-276. http://geodesic.mathdoc.fr/item/SMJ2_2006_32_2-3_a8/