151. Associated Prime Divisors in the Sense of Krull
- Author
-
Richard A. Kuntz
- Subjects
Ring (mathematics) ,General Mathematics ,010102 general mathematics ,Commutative ring ,Regular local ring ,Characterization (mathematics) ,Type (model theory) ,01 natural sciences ,Combinatorics ,Associated prime ,Krull's principal ideal theorem ,0103 physical sciences ,010307 mathematical physics ,Krull dimension ,0101 mathematics ,Mathematics - Abstract
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,Rdenotes 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 ofR.On the whole, our terminology will be that of [9]. We do, however, take exception with [9] in two instances, viz.
- Published
- 1972