Journal article
Star operations and primitive polynomials
Communications in Algebra, Vol.27(7), pp.3137-3142
01/01/1999
DOI: 10.1080/00927879908826616
Abstract
Let D be an integral domain with quotient field K. We investigate conditions under which certain primitive polynomials are products of principal primes. Let * be a finite character star operation on D[X] (e.g., * = d or t) and let * also denote the star operation induced on D by I * = (I[X]) * ∩ K where I denotes a nonzero fractional ideal of D. Then the following conditions are equivalent: (1) D is integrally closed and each *-invertible *-ideal is principal, (2) If P is a prime upper to 0 containing an f ∈ D[X] with , then P is principal, and (3) For f ∈ D[X] with f is a product of principal primes.
Details
- Title: Subtitle
- Star operations and primitive polynomials
- Creators
- D.D Anderson - Department of Mathematics , The University of IowaMuhammad Zafrullah - Department of Mathematics , The University of Iowa
- Resource Type
- Journal article
- Publication Details
- Communications in Algebra, Vol.27(7), pp.3137-3142
- Publisher
- Gordon and Breach Science Publishers Ltd
- DOI
- 10.1080/00927879908826616
- ISSN
- 0092-7872
- eISSN
- 1532-4125
- Language
- English
- Date published
- 01/01/1999
- Academic Unit
- Mathematics
- Record Identifier
- 9983986086602771
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