Abstract
Let I be a monomial ideal in a polynomial ring with two indeterminates over a field. Assume I is contained in the integral closure of some ideal that is generated by two elements from the generating set of I. We produce sharp upper bounds for each of the reduction number and the Ratliff-Rush reduction number of the ideal I. Under certain hypotheses, we give the exact values of these reduction numbers, and we provide an explicit method for obtaining these sharp upper bounds.
Original language | English |
---|---|
Article number | 2050201 |
Journal | Journal of Algebra and Its Applications |
Volume | 19 |
Issue number | 10 |
DOIs | |
Publication status | Published - Oct 29 2020 |
Keywords
- Ratliff-Rush closure
- Reduction number
ASJC Scopus subject areas
- Algebra and Number Theory
- Applied Mathematics