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Radicals Of Polynomial Rings

Published online by Cambridge University Press:  20 November 2018

S. A. Amitsur
S. A. Amitsur*
Affiliation:
Hebrew University, Jerusalem, Israel
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Introduction. Let R be a ring and let R[x] be the ring of all polynomials in a commutative indeterminate x over R. Let J(R) denote the Jacobson radical (5) of the ring R and let L(R) be the lower radical (4) of R. The main object of the present note is to determine the radicals J(R[x]) and L(R[x]). The Jacobson radical J(R[x]) is shown to be a polynomial ring N[x] over a nil ideal N of R and the lower radical L(R[x]) is the polynomial ring L(R)[x].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 355 - 361
Copyright
Copyright © Canadian Mathematical Society 1956

References

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