Journal article
Length functions in commutative rings with zero divisors
Communications in Algebra, Vol.45(4), pp.1584-1600
2017
DOI: 10.1080/00927872.2016.1222400
Abstract
Let R be a commutative ring. We investigate several functions which measure the length of factorizations of an element of R. Some of these functions are functionsare l, lU : R → N0 (for R atomic)and L, LU : R → N0 ∪ {∞} where l(x) = lU(x) = L(x) = LU(x) = 0 for x a unit,andfor x not aunit l(x)= inf{n | x= x1 • •• xn, xi irreducible}, lU(x)= inf{n | x = y1 • •• ym⌈x1 • •• xn⌉, a U-decomposition}, L(x) = sup{n | x = x1 • •• xn, xi a nonunit}, and LU (x) = sup{n | x = y1 • •• ym⌈x1 • •• xn⌉ a U-factorization}. For R satisfying the ascending chain condition on principal ideals, we consider the ordinal-valued function L obtained by recursively defining L(x) to be the least ordinal strictly greater than L(y) for each proper divisor y of x. © 2017, Copyright © Taylor & Francis.
Details
- Title: Subtitle
- Length functions in commutative rings with zero divisors
- Creators
- D.D. Anderson - University of IowaJ.R. Juett - Texas State University
- Resource Type
- Journal article
- Publication Details
- Communications in Algebra, Vol.45(4), pp.1584-1600
- Publisher
- Taylor and Francis Inc.
- DOI
- 10.1080/00927872.2016.1222400
- ISSN
- 0092-7872
- Language
- English
- Date published
- 2017
- Academic Unit
- Mathematics
- Record Identifier
- 9984230420802771
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