scholarly journals Ideals of Reduction Number Two

2021 ◽  
Author(s):  
Shinya Kumashiro
Keyword(s):  
Reduction Number

scholarly journals Borel-fixed ideals and reduction number

2003 ◽  
Vol 270 (1) ◽  
pp. 335-346 ◽  
Author(s):  
Lê Tuân Hoa ◽  
Ngô Viêt Trung
Keyword(s):  
Reduction Number

scholarly journals Analysis of dengue model with fractal-fractional Caputo–Fabrizio operator

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Fatmawati ◽  
Muhammad Altaf Khan ◽  
Cicik Alfiniyah ◽  
Ebraheem Alzahrani
Keyword(s):  
Statistical Data ◽  
Dengue Infection ◽  
Fractional Operator ◽  
Novel Approach ◽  
Reduction Number ◽  
Best Fitting ◽  
The Stability ◽  
Parameter Values ◽  
Graphical Illustration ◽  
Stability Results

AbstractIn this work, we study the dengue dynamics with fractal-factional Caputo–Fabrizio operator. We employ real statistical data of dengue infection cases of East Java, Indonesia, from 2018 and parameterize the dengue model. The estimated basic reduction number for this dataset is $\mathcal{R}_{0}\approx2.2020$ R 0 ≈ 2.2020 . We briefly show the stability results of the model for the case when the basic reproduction number is $\mathcal{R}_{0} <1$ R 0 < 1 . We apply the fractal-fractional operator in the framework of Caputo–Fabrizio to the model and present its numerical solution by using a novel approach. The parameter values estimated for the model are used to compare with fractal-fractional operator, and we suggest that the fractal-fractional operator provides the best fitting for real cases of dengue infection when varying the values of both operators’ orders. We suggest some more graphical illustration for the model variables with various orders of fractal and fractional.

Reduction numbers and Hilbert polynomials of ideals in higher dimensional CohenMacaulay local rings

1992 ◽  
Vol 111 (1) ◽  
pp. 47-56 ◽  
Author(s):  
Yinghwa Wu
Keyword(s):  
Local Ring ◽  
Residue Field ◽  
Primary Ideal ◽  
Local Rings ◽  
Hilbert Polynomials ◽  
Higher Dimensional ◽  
Reduction Number ◽  
Minimal Reduction ◽  
System Of Parameters

Throughout, (R, m) will denote a d-dimensional CohenMacaulay (CM for short) local ring having an infinite residue field and I an m-primary ideal in R. Recall that an ideal J I is said to be a reduction of I if Ir+1 = JIr for some r 0, and a reduction J of I is called a minimal reduction of I if J is generated by a system of parameters. The concepts of reduction and minimal reduction were first introduced by Northcott and Rees12. If J is a reduction of I, define the reduction number of I with respect to J, denoted by rj(I), to be min {r 0 Ir+1 = JIr}. The reduction number of I is defined as r(I) = min {rj(I)J is a minimal reduction of I}. The reduction number r(I) is said to be independent if r(I) = rj(I) for every minimal reduction J of I.

scholarly journals An Upper Bound on the Reduction Number of an Ideal

2009 ◽  
Vol 37 (5) ◽  
pp. 1690-1699 ◽  
Author(s):  
Yayoi Kinoshita ◽  
Koji Nishida ◽  
Kensuke Sakata ◽  
Ryuta Shinya
Keyword(s):  
Upper Bound ◽  
Reduction Number

scholarly journals The depth of the associated graded ring of ideals with any reduction number

2004 ◽  
Vol 276 (1) ◽  
pp. 168-179 ◽  
Author(s):  
Ian Aberbach ◽  
Laura Ghezzi ◽  
Huy Tài Hà
Keyword(s):  
Associated Graded Ring ◽  
Graded Ring ◽  
Reduction Number

scholarly journals The normal reduction number of two-dimensional cone-like singularities

2021 ◽  
Vol 149 (11) ◽  
pp. 4569-4581
Author(s):  
Tomohiro Okuma ◽  
Kei-ichi Watanabe ◽  
Ken-ichi Yoshida
Keyword(s):  
Two Dimensional ◽  
Dimensional Cone ◽  
Reduction Number

scholarly journals On the reduction number of some graded algebras

1999 ◽  
Vol 127 (5) ◽  
pp. 1257-1263 ◽  
Author(s):  
Henrik Bresinsky ◽  
Lê Tuân Hoa
Keyword(s):  
Graded Algebras ◽  
Reduction Number

Pullback of the Normal Module of Ideals with Low Codimension

2021 ◽  
Author(s):  
Cleto B Miranda-Neto
Keyword(s):  
Algebraic Geometry ◽  
Commutative Algebra ◽  
Difficult Problem ◽  
Natural Projection ◽  
Analytic Spread ◽  
Reduction Number ◽  
Numerical Invariants ◽  
Special Classes

Abstract The normal module (or sheaf) of an ideal is a celebrated object in commutative algebra and algebraic geometry. In this paper, we prove results about its pullback under the natural projection, focusing on subtle numerical invariants such as, for instance, the reduction number. For certain codimension 2 perfect ideals, we show that the pullback has reduction number two. This is of interest since the determination of this invariant in the context of modules (even for special classes) is a mostly open, difficult problem. The analytic spread is also computed. Finally, for codimension 3 Gorenstein ideals, we determine the depth of the pullback, and we also consider a broader class of ideals provided that the Auslander transpose of the conormal module is almost Cohen–Macaulay.

Sign in / Sign up

Export Citation Format

Share Document