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Associated Prime Divisors in the Sense of Krull

Published online by Cambridge University Press:  20 November 2018

Richard A. Kuntz
Richard A. Kuntz*
Affiliation:
Monmouth College, West Long Branch, New Jersey
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In a recent paper by Douglas Underwood [8] several definitions of “associated prime divisors” were discussed and shown to be unique. In this note we produce a fifth type, which is due to W. Krull, and is found in his classical paper [2] and further discussed by B. Banaschewski in [1]. Historically this characterization considerably predates the other four definitions.

Throughout this note, R denotes a commutative ring with unity, and all ideals and elements are assumed to be in such a ring. We shall let upper case letters, most frequently the beginning of the alphabet, denote ideals and lower case letters, elements of R. On the whole, our terminology will be that of [9]. We do, however, take exception with [9] in two instances, viz.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 5 , October 1972 , pp. 808 - 818
Copyright
Copyright © Canadian Mathematical Society 1972

References

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