Weakly factorial domains and groups of divisibility

D.D. Anderson; M. Zafrullah

doi:10.1090/S0002-9939-1990-1021893-7

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Weakly factorial domains and groups of divisibility

Journal article

Open access

Peer reviewed

Weakly factorial domains and groups of divisibility

D.D. Anderson and M. Zafrullah

Proceedings of the American Mathematical Society, Vol.109, pp.907-913

1990

DOI: 10.1090/S0002-9939-1990-1021893-7

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Abstract

An integral domain R is said to be weakly factorial if every nonunit of R is a product of primary elements. We give several conditions equivalent to R being weakly factorial. For example, we show that the following conditions are equivalent: (1) R is weakly factorial; (2) every convex directed subgroup of the group of divisibility of R is a cardinal summand; (3) if P is a prime ideal of R minimal over a proper principal ideal (x), then P has height one and (x)p ⋂ R is principal; (4) R = ⋂Rp, where the intersection runs over the height-one primes of R, is locally finite, and the i-class group of R is trivial. © 1990 American Mathematical Society.

Details

Title: Subtitle: Weakly factorial domains and groups of divisibility
Creators: D.D. Anderson
M. Zafrullah
Resource Type: Journal article
Publication Details: Proceedings of the American Mathematical Society, Vol.109, pp.907-913
DOI: 10.1090/S0002-9939-1990-1021893-7
ISSN: 0002-9939
Language: English
Date published: 1990
Academic Unit: Mathematics
Record Identifier: 9984230421402771

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