Journal article
Annihilating content polynomials and EM-rings
Journal of Algebra and its Applications, Vol.21(5), 2250092
2021
DOI: 10.1142/S021949882250092X
Abstract
Let R be a commutative ring. A polynomial f R[X] is an annihilating content (AC) polynomial if f = ag where a R and g R[X] is a nonzerodivisor and R is an EM-ring if each f R[X] is an AC polynomial. In this paper, we investigate AC polynomials and EM-rings and extensions to modules. For example, we show that R is an EM-ring if and only if every linear polynomial is an AC polynomial if and only if for each finitely generated ideal I of R, I = aJ where a R and J is a finitely generated ideal of R with (0: J) = 0. Special attention is given to the case when R is Noetherian where such rings are characterized by the property that each associated prime is principal. © 2022 World Scientific Publishing Company.
Details
- Title: Subtitle
- Annihilating content polynomials and EM-rings
- Creators
- D.D. Anderson - University of IowaE. Abuosba - University of JordanM. Ghanem - University of Jordan
- Resource Type
- Journal article
- Publication Details
- Journal of Algebra and its Applications, Vol.21(5), 2250092
- Publisher
- World Scientific
- DOI
- 10.1142/S021949882250092X
- ISSN
- 0219-4988
- Language
- English
- Date published
- 2021
- Academic Unit
- Mathematics
- Record Identifier
- 9984230421102771
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