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# Coefficients ideals for arbitrary ideals

 Grant number: 12/01084-0 Support type: Scholarships in Brazil - Doctorate Effective date (Start): July 01, 2013 Effective date (End): July 31, 2015 Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra Principal Investigator: Victor Hugo Jorge Pérez Grantee: Thiago Henrique de Freitas Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil Associated scholarship(s): 13/20723-7 - Finiteness properties and Artinianness of formal local cohomology modules dened by a PAIs of ideals, BE.EP.DR Abstract Kishor Shah proved the existence and uniqueness of a chain of ideals between the ideals $I$ the ring $R$ and the integral closure of the same, these ideals preserve the first $k +1$ the Hilbert coefficients of $I$, i.e., there are ideals $I_k$ containing the ideal $I$, for every integer $k = 1, \ ldots, d$ such that $I \subset I_ d \subset \ldots \subset I_1 \subset \overline {I}$ and$e_i (I, R) = e_i (I_ {\lbrace k \rbrace}, R)$, for every integer $i = 0, \ldots, k$. The integer $e_i$(I, R)$is called the$ i$-th Hilbert coefficient of the ideal$ I $and$ I_ {\lbrace k \rbrace}$is called$k$-th coefficient of the ideal$$. He also obtain the structure of each$I_{\lbrace k \rbrace}$of$ I$.In our project we intend to generalize the result of Kishor Shah in the case when the ideal$I\$ is an arbitrary ideal. (AU)

Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
FREITAS, THIAGO H.; JORGE PEREZ, VICTOR H. On the endomorphism ring and Cohen-Macaulayness of local cohomology defined by a pair of ideals. CZECHOSLOVAK MATHEMATICAL JOURNAL, v. 69, n. 2, p. 453-470, JUN 2019. Web of Science Citations: 0.
FREITAS, T. H.; JORGE PEREZ, V. H. Artinianness and finiteness of formal local cohomology modules with respect to a pair of ideals. BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY, v. 58, n. 2, p. 319-340, JUN 2017. Web of Science Citations: 1.
FREITAS, T. H.; PEREZ, V. H. JORGE. ON FORMAL LOCAL COHOMOLOGY MODULES WITH RESPECT TO A PAIR OF IDEALS. JOURNAL OF COMMUTATIVE ALGEBRA, v. 8, n. 3, p. 337-366, FAL 2016. Web of Science Citations: 2.