科研之友
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摘要
Let I be a monomial ideal with minimal monomial generators m(1) ,..., m(s), and assume that deg (m(1)) >= deg (m(2)) >= ... >= deg (m(s)). Among other things, we prove that the arithmetic degree of I is bounded above by deg (m(1)) ... deg (m(mht(1))), where mht(I) is the maximal height of associated primes of I. This bound is shaper than the one given in [12] and more natural than the one given in [9]. In addition, we point out that adeg(I) not equal adeg(Gin(I)) in general and conjecture that adeg(I) = adeg(Gin(I)) if and only if R/I is sequentially Cohen-Macaulay.
- 出版日期2016
- 单位苏州大学
