Journal article
Commutative group rings that are présimplifiable or domainlike
Journal of Algebra and its Applications, Vol.16(1), 1750019
2017
DOI: 10.1142/S0219498817500190
Abstract
A commutative ring A is called présimplifiable (respectively, domainlike) if whenever a,b A with a = ba, then either a = 0 or b is a unit in A (respectively, 0 is a primary ideal of A). Let A be a commutative ring and G be a nonzero abelian group. For the group ring A[G], we prove that if G is torsion, then A[G] is présimplifiable (respectively, domainlike) if and only if A is présimplifiable (respectively, domainlike) and G is p-primary with p J(A) (respectively, p nil(A)). If G is torsion-free, then A[G] is présimplifiable if and only if A[G] is domainlike if and only if A is domainlike. Finally, if G is mixed, A[G] is présimplifiable (respectively, domainlike) if and only if A is domainlike and the torsion subgroup of G is p-primary with p J(A) (respectively, p nil(A)). © 2017 World Scientific Publishing Company.
Details
- Title: Subtitle
- Commutative group rings that are présimplifiable or domainlike
- Creators
- D.D. Anderson - University of IowaO.A. Al-Mallah
- Resource Type
- Journal article
- Publication Details
- Journal of Algebra and its Applications, Vol.16(1), 1750019
- Publisher
- World Scientific Publishing Co. Pte Ltd
- DOI
- 10.1142/S0219498817500190
- ISSN
- 0219-4988
- Language
- English
- Date published
- 2017
- Academic Unit
- Mathematics
- Record Identifier
- 9984230627402771
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