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- Title
On the structure of ideals in a family of skew polynomial rings.
- Authors
Shahoseini, Ehsan; Dastbasteh, Reza; Dinh, Hai Q.; Mousavi, Hamed
- Abstract
In this paper, we study the structure of the skew polynomial ring R = ( p + u p) [ x ; ] and its quotient ring R n = R / 〈 x n − 1 〉 , where p is an odd prime number, u 2 = 0 , and (u) = − u. We give an explicit structure of the ideals in R and R n and propose an algorithm to characterize them. We identify the structure of prime, maximal, and primary ideals in these rings. In particular, we prove that this group ring is not Laskerian.
- Subjects
POLYNOMIAL rings; QUOTIENT rings; PRIME numbers; ODD numbers; PRIME ideals; CYCLIC codes
- Publication
Journal of Algebra & Its Applications, 2024, Vol 23, Issue 8, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498824501743