On the uniform behaviour of the Frobenius closures of ideals

K. Khashyarmanesh. "On the uniform behaviour of the Frobenius closures of ideals." Colloquium Mathematicae 109.1 (2007): 1-7. <http://eudml.org/doc/283979>.

@article{K2007,
abstract = {Let be a proper ideal of a commutative Noetherian ring R of prime characteristic p and let Q() be the smallest positive integer m such that $(^\{F\})^\{[p^m]\} = ^\{[p^m]\}$, where $^\{F\}$ is the Frobenius closure of . This paper is concerned with the question whether the set $\{Q(^\{[p^m]\}) : m ∈ ℕ₀\}$ is bounded. We give an affirmative answer in the case that the ideal is generated by an u.s.d-sequence c₁,..., cₙ for R such that (i) the map $R/∑_\{j=1\}^\{n\} Rc_j → R/∑_\{j = 1\}^\{n\} Rc²_j$ induced by multiplication by c₁...cₙ is an R-monomorphism; (ii) for all $ ∈ ass(c₁^j, ..., cₙ^j)$, c₁/1,..., cₙ/1 is a $R_\{\}$-filter regular sequence for $R_\{\}$ for j ∈ 1,2.},
author = {K. Khashyarmanesh},
journal = {Colloquium Mathematicae},
keywords = {commutative noetherian ring; prime characteristic; Frobenius homomorphism; skew polynomial ring; local cohomology module; Koszul homology; u.s.-sequence; filter regular sequence},
language = {eng},
number = {1},
pages = {1-7},
title = {On the uniform behaviour of the Frobenius closures of ideals},
url = {http://eudml.org/doc/283979},
volume = {109},
year = {2007},
}

TY - JOUR
AU - K. Khashyarmanesh
TI - On the uniform behaviour of the Frobenius closures of ideals
JO - Colloquium Mathematicae
PY - 2007
VL - 109
IS - 1
SP - 1
EP - 7
AB - Let be a proper ideal of a commutative Noetherian ring R of prime characteristic p and let Q() be the smallest positive integer m such that $(^{F})^{[p^m]} = ^{[p^m]}$, where $^{F}$ is the Frobenius closure of . This paper is concerned with the question whether the set ${Q(^{[p^m]}) : m ∈ ℕ₀}$ is bounded. We give an affirmative answer in the case that the ideal is generated by an u.s.d-sequence c₁,..., cₙ for R such that (i) the map $R/∑_{j=1}^{n} Rc_j → R/∑_{j = 1}^{n} Rc²_j$ induced by multiplication by c₁...cₙ is an R-monomorphism; (ii) for all $ ∈ ass(c₁^j, ..., cₙ^j)$, c₁/1,..., cₙ/1 is a $R_{}$-filter regular sequence for $R_{}$ for j ∈ 1,2.
LA - eng
KW - commutative noetherian ring; prime characteristic; Frobenius homomorphism; skew polynomial ring; local cohomology module; Koszul homology; u.s.-sequence; filter regular sequence
UR - http://eudml.org/doc/283979
ER -