Journal article
Armendariz rings and gaussian rings
Communications in Algebra, Vol.26(7), pp.2265-2272
01/01/1998
DOI: 10.1080/00927879808826274
Abstract
We prove a number of results concerning Armendariz rings and Gaussian rings. Recall that a (commutative) ring R is (Gaussian) Armendariz if for two polynomials f,g∈R[X] (the ideal of R generated by the coefficients of f g is the product of the ideals generated by the coefficients of f and g) fg = 0 implies a i b j =0 for each coefficient a i of f and b j of g. A number of examples of Armendariz rings are given. We show that R Armendariz implies that R[X] is Armendariz and that for R von Neumann regularR is Armendariz if and only if R is reduced. We show that R is Gaussian if and only if each homomorphic image of R is Armendariz. Characterizations of when R[X] and R[X] are Gaussian are given.
Details
- Title: Subtitle
- Armendariz rings and gaussian rings
- Creators
- D.D Anderson - Department of Mathematics , The University of IowaVictor Camillo - Department of Mathematics , The University of Iowa
- Resource Type
- Journal article
- Publication Details
- Communications in Algebra, Vol.26(7), pp.2265-2272
- Publisher
- Gordon and Breach Science Publishers Ltd
- DOI
- 10.1080/00927879808826274
- ISSN
- 0092-7872
- eISSN
- 1532-4125
- Language
- English
- Date published
- 01/01/1998
- Academic Unit
- Mathematics
- Record Identifier
- 9983985864902771
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