scholarly journals (Non)Vanishing results on local cohomology of valuation rings

2017 ◽  
Vol 479 ◽  
pp. 413-436
Author(s):  
Rankeya Datta
Keyword(s):  
Local Cohomology ◽  
Valuation Rings

scholarly journals On three-variable expanders over finite valuation rings

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Le Quang Ham ◽  
Nguyen Van The ◽  
Phuc D. Tran ◽  
Le Anh Vinh
Keyword(s):  
Valuation Ring ◽  
Product Type ◽  
Quadratic Polynomial ◽  
Valuation Rings

AbstractLet {\mathcal{R}} be a finite valuation ring of order {q^{r}}. In this paper, we prove that for any quadratic polynomial {f(x,y,z)\in\mathcal{R}[x,y,z]} that is of the form {axy+R(x)+S(y)+T(z)} for some one-variable polynomials {R,S,T}, we have|f(A,B,C)|\gg\min\biggl{\{}q^{r},\frac{|A||B||C|}{q^{2r-1}}\bigg{\}}for any {A,B,C\subset\mathcal{R}}. We also study the sum-product type problems over finite valuation ring {\mathcal{R}}. More precisely, we show that for any {A\subset\mathcal{R}} with {|A|\gg q^{r-\frac{1}{3}}} then {\max\{|AA|,|A^{d}+A^{d}|\}}, {\max\{|A+A|,|A^{2}+A^{2}|\}}, {\max\{|A-A|,|AA+AA|\}\gg|A|^{\frac{2}{3}}q^{\frac{r}{3}}}, and {|f(A)+A|\gg|A|^{\frac{2}{3}}q^{\frac{r}{3}}} for any one variable quadratic polynomial f.

scholarly journals Valuation rings are derived splinters

2021 ◽  
Author(s):  
Benjamin Antieau ◽  
Rankeya Datta
Keyword(s):  
Valuation Rings

scholarly journals Artinianness of local cohomology modules

2014 ◽  
Vol 52 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Moharram Aghapournahr ◽  
Leif Melkersson
Keyword(s):  
Local Cohomology ◽  
Local Cohomology Modules ◽  
Cohomology Modules

On the associated primes of local cohomology modules

1999 ◽  
Vol 27 (12) ◽  
pp. 6191-6198 ◽  
Author(s):  
K. Khashyarmanesh ◽  
Sh Salarian
Keyword(s):  
Local Cohomology ◽  
Associated Primes ◽  
Local Cohomology Modules ◽  
Cohomology Modules

scholarly journals LOCAL RINGS OF BOUNDED MODULE TYPE ARE ALMOST MAXIMAL VALUATION RINGS

2005 ◽  
Vol 33 (8) ◽  
pp. 2851-2855 ◽  
Author(s):  
François Couchot
Keyword(s):  
Local Rings ◽  
Valuation Rings ◽  
Module Type

scholarly journals Algebraic series and valuation rings over nonclosed fields

2008 ◽  
Vol 212 (8) ◽  
pp. 1996-2010 ◽  
Author(s):  
Steven Dale Cutkosky ◽  
Olga Kashcheyeva
Keyword(s):  
Valuation Rings

scholarly journals Local cohomology of certain Rees- and form-rings, I

1983 ◽  
Vol 81 (1) ◽  
pp. 29-57 ◽  
Author(s):  
Markus Brodmann
Keyword(s):  
Local Cohomology

Finitely generated modules over valuation rings

1984 ◽  
Vol 12 (15) ◽  
pp. 1795-1812 ◽  
Author(s):  
Luigi Salce ◽  
Paolo Zanardo
Keyword(s):  
Finitely Generated ◽  
Valuation Rings ◽  
Finitely Generated Modules
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