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In algebra, a central polynomial for n-by- … In algebra, a central polynomial for n-by-n matrices is a polynomial in non-commuting variables that is non-constant but yields a scalar matrix whenever it is evaluated at n-by-n matrices. That such polynomials exist for any square matrices was discovered in 1970 independently by Formanek and Razmyslov. The term "central" is because the evaluation of a central polynomial has the image lying in the center of the matrix ring over any commutative ring. The notion has an application to the theory of polynomial identity rings. Example: is a central polynomial for 2-by-2-matrices. Indeed, by the Cayley–Hamilton theorem, one has that for any 2-by-2-matrices x and y. has that for any 2-by-2-matrices x and y.
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| rdfs:comment |
In algebra, a central polynomial for n-by- … In algebra, a central polynomial for n-by-n matrices is a polynomial in non-commuting variables that is non-constant but yields a scalar matrix whenever it is evaluated at n-by-n matrices. That such polynomials exist for any square matrices was discovered in 1970 independently by Formanek and Razmyslov. The term "central" is because the evaluation of a central polynomial has the image lying in the center of the matrix ring over any commutative ring. The notion has an application to the theory of polynomial identity rings.o the theory of polynomial identity rings.
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| rdfs:label |
Central polynomial
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