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Prime and maximal ideals in polynomial rings

Published online by Cambridge University Press:  18 May 2009

Miguel Ferrero
Miguel Ferrero
Affiliation:
Instituto de Matemática, Universidade Federal do Rio Grande do Sul, 91509-900-Porto Alegre, RS, Brazil
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In this paper we study prime and maximal ideals in a polynomial ring R[X], where R is a ring with identity element. It is well-known that to study many questions we may assume Ris prime and consider just R-disjoint ideals. We give a characterizaton for an R-disjoint ideal to be prime. We study conditions under which there exists an R-disjoint ideal which is a maximal ideal and when this is the case how to determine all such maximal ideals. Finally, we prove a theorem giving several equivalent conditions for a maximal ideal to be generated by polynomials of minimal degree.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 37 , Issue 3 , September 1995 , pp. 351 - 362
Copyright
Copyright © Glasgow Mathematical Journal Trust 1995

References

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