Regular sequences and mahler functions

1996 ◽  
pp. 150-175
Author(s):  
Kumiko Nishioka
Keyword(s):  
Regular Sequences ◽  
Mahler Functions

Ubiquity of relative regular sequences and proper sequences

K-Theory ◽  
1994 ◽  
Vol 8 (1) ◽  
pp. 81-106 ◽  
Author(s):  
Mihai Cipu ◽  
Mario Fiorentini
Keyword(s):  
Regular Sequences

The Main Case for Regular Sequences

2001 ◽  
pp. 96-104
Author(s):  
Günter Scheja ◽  
Uwe Storch
Keyword(s):  
Regular Sequences

The Main Case for Generic Regular Sequences

2001 ◽  
pp. 85-95
Author(s):  
Günter Scheja ◽  
Uwe Storch
Keyword(s):  
Regular Sequences

scholarly journals Some New Methods in the Theory of $m$-Quasi-Invariants

10.37236/1877 ◽  
2005 ◽  
Vol 11 (2) ◽  
Author(s):  
J. Bell ◽  
A. M. Garsia ◽  
N. Wallach
Keyword(s):  
Symmetric Functions ◽  
Free Module ◽  
Finitely Generated ◽  
Graded Algebras ◽  
New Approach ◽  
Elementary Symmetric Functions ◽  
New Methods ◽  
Regular Sequences

We introduce here a new approach to the study of $m$-quasi-invariants. This approach consists in representing $m$-quasi-invariants as $N^{tuples}$ of invariants. Then conditions are sought which characterize such $N^{tuples}$. We study here the case of $S_3$ $m$-quasi-invariants. This leads to an interesting free module of triplets of polynomials in the elementary symmetric functions $e_1,e_2,e_3$ which explains certain observed properties of $S_3$ $m$-quasi-invariants. We also use basic results on finitely generated graded algebras to derive some general facts about regular sequences of $S_n$ $m$-quasi-invariants

scholarly journals Regular sequences and synchronized sequences in abstract numeration systems

2022 ◽  
Vol 101 ◽  
pp. 103475
Author(s):  
Émilie Charlier ◽  
Célia Cisternino ◽  
Manon Stipulanti
Keyword(s):  
Regular Sequences ◽  
Numeration Systems

scholarly journals Proregular sequences, local cohomology, and completion

2003 ◽  
Vol 92 (2) ◽  
pp. 161 ◽  
Author(s):  
Peter Schenzel
Keyword(s):  
Noetherian Ring ◽  
Local Cohomology ◽  
Čech Complex ◽  
Regular Sequences ◽  
Local Cohomology Modules ◽  
Derived Functors ◽  
Adic Completion ◽  
Cech Complex ◽  
Cohomology Modules ◽  
The Ideal

As a certain generalization of regular sequences there is an investigation of weakly proregular sequences. Let $M$ denote an arbitrary $R$-module. As the main result it is shown that a system of elements $\underline x$ with bounded torsion is a weakly proregular sequence if and only if the cohomology of the Čech complex $\check C_{\underline x} \otimes M$ is naturally isomorphic to the local cohomology modules $H_{\mathfrak a}^i(M)$ and if and only if the homology of the co-Čech complex $\mathrm{RHom} (\check C_{\underline x}, M)$ is naturally isomorphic to $\mathrm{L}_i \Lambda^{\mathfrak a}(M),$ the left derived functors of the $\mathfrak a$-adic completion, where $\mathfrak a$ denotes the ideal generated by the elements $\underline x$. This extends results known in the case of $R$ a Noetherian ring, where any system of elements forms a weakly proregular sequence of bounded torsion. Moreover, these statements correct results previously known in the literature for proregular sequences.

scholarly journals Syzygetic ideals, regular sequences, and a question of Simis

1989 ◽  
Vol 121 (2) ◽  
pp. 310-314 ◽  
Author(s):  
Javier Barja ◽  
Antonio G Rodicio
Keyword(s):  
Regular Sequences
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