Geodesic
Sets of Generators of a Commutative and Associative Algebra(1)
Canadian mathematical bulletin, Tome 14 (1971) no. 3, pp. 315-319

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Let A be a finite dimensional commutative and associative algebra with identity, over a field K. We assume also that A is generated by one element and consequently, isomorphic to a quotient algebra of the polynomial algebra K[X]. If A=K[a] and bi =fi(A), fi(X) ∊ K[X], 1≤i≤r we find necessary and sufficient conditions which should be satisfied by fi(X) in order that A = K[b 1, ..., br ].The result can be stated as a theorem about matrices. As a special case we obtain a recent result of Thompson [4].In fact this last result was established earlier by Mirsky and Rado [3]. I am grateful to the referee for supplying this reference. 
Sets of Generators of a Commutative and Associative Algebra(1). Canadian mathematical bulletin, Tome 14 (1971) no. 3, pp. 315-319. doi: 10.4153/CMB-1971-058-7
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1971-058-7/}
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