No CrossRef data available.
Article contents
Sets of Generators of a Commutative and Associative Algebra(1)
Published online by Cambridge University Press: 20 November 2018
Abstract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
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[b1, …, 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.
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 1971
Footnotes
(1)
The preparation of this paper was supported in part by National Research Council Grant A-5285.
References
3.
Mirsky, L. and Rado, R., A note on matrix polynomials, Quart. J. Math. Oxford Ser. (2) 8 (1957), 128-132.Google Scholar
4.
Thompson, R. C., On the matrices A and f(A), Canad. Math. Bull. 12 (1969), 581-587.Google Scholar
You have
Access