Are complete intersections complete intersections?
| Autor: | David A. Jorgensen, Raymond C. Heitmann |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Principal ideal ring
Discrete mathematics Algebra and Number Theory Regular sequence Mathematics::Commutative Algebra 010102 general mathematics Boolean ring Commutative ring Regular local ring Commutative Algebra (math.AC) Mathematics - Commutative Algebra 01 natural sciences Completion Combinatorics Regular ring 0103 physical sciences FOS: Mathematics 010307 mathematical physics Ideal (ring theory) 0101 mathematics 13J10 13C40 14M10 Complete intersection Quotient ring Mathematics |
| Zdroj: | Journal of Algebra. 371:276-299 |
| ISSN: | 0021-8693 |
| DOI: | 10.1016/j.jalgebra.2012.08.006 |
| Popis: | A commutative local ring is generally defined to be a complete intersection if its completion is isomorphic to the quotient of a regular local ring by an ideal generated by a regular sequence. It has not previously been determined whether or not such a ring is necessarily itself the quotient of a regular ring by an ideal generated by a regular sequence. In this article, it is shown that if a complete intersection is a one dimensional integral domain, then it is such a quotient. However, an example is produced of a three dimensional complete intersection domain which is not a homomorphic image of a regular local ring, and so the property does not hold in general. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect