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Specialization of integral closure of ideals by general elements.
- Source :
-
Proceedings of the American Mathematical Society . May2024, Vol. 152 Issue 5, p1893-1906. 14p. - Publication Year :
- 2024
-
Abstract
- In this paper, we prove a result similar to results of Itoh [J. Algebra 150 (1992), pp. 101–117] and Hong-Ulrich [J. Lond. Math. Soc. (2) 90 (2014), pp. 861–878], proving that integral closure of an ideal is compatible with specialization by a general element of that ideal for ideals of height at least two in a large class of rings. Moreover, we show integral closure of sufficiently large powers of the ideal is compatible with specialization by a general element of the original ideal. In a polynomial ring over an infinite field, we give a class of squarefree monomial ideals for which the integral closure is compatible with specialization by a general linear form. [ABSTRACT FROM AUTHOR]
- Subjects :
- *POLYNOMIAL rings
*INTEGRALS
*ALGEBRA
Subjects
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 152
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 176473199
- Full Text :
- https://doi.org/10.1090/proc/16697