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Prime essential rings

Published online by Cambridge University Press:  20 January 2009

B. J. Gardner  and
P. N. Stewart
B. J. Gardner
Affiliation:
Mathematics DepartmentUniversity of TasmaniaHobart, Tasmania 7001Australia
P. N. Stewart
Affiliation:
Department of Mathematics, Statistics and Computing ScienceDalhousie UniversityHalifax, Nova ScotiaCanadaB3H 3J5
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A ring R is prime essential if R is semiprime and for each prime ideal P of R, P ∩ I ≠0 whenever I is a nonzero two-sided ideal of R. Examples of prime essential rings include rings of continuous functions and infinite products modulo infinite sums. We show that the class of prime essential rings is closed under many familiar operations; in particular, we consider polynomial rings, matix rings, fixed rings and skew group rings. Also, we explore the relationship between prime essential rings and special radical classes, and we demonstrate how prime essential rings can be used to construct radical classes which are not special.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 34 , Issue 2 , June 1991 , pp. 241 - 250
Copyright
Copyright © Edinburgh Mathematical Society 1991

References

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