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Lattice of ideals of the polynomial ring over a commutative chain ring.
- Source :
-
Applicable Algebra in Engineering, Communication & Computing . Aug2015, Vol. 26 Issue 4, p317-346. 30p. - Publication Year :
- 2015
-
Abstract
- Let $$R$$ be a commutative chain ring. We use a variation of Gröbner bases to study the lattice of ideals of $$R[x]$$ . Let $$I$$ be a proper ideal of $$R[x]$$ . We are interested in the following two questions: When is $$R[x]/I$$ Frobenius? When is $$R[x]/I$$ Frobenius and local? We develop algorithms for answering both questions. When the nilpotency of $$\text {rad}\,R$$ is small, the algorithms provide explicit answers to the questions. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09381279
- Volume :
- 26
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Applicable Algebra in Engineering, Communication & Computing
- Publication Type :
- Academic Journal
- Accession number :
- 108467968
- Full Text :
- https://doi.org/10.1007/s00200-015-0253-8