Enumerating graded ideals in graded rings associated to free nilpotent Lie rings

Enumerating graded ideals in graded rings associated to free nilpotent Lie rings Math. Z. https://doi.org/10.1007/s00209-018-2062-9 Mathematische Zeitschrift Enumerating graded ideals in graded rings associated to free nilpotent Lie rings 1 2 Seungjai Lee · Christopher Voll Received: 14 June 2016 / Accepted: 12 February 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract We compute the zeta functions enumerating graded ideals in the graded Lie rings associated with the free d-generator Lie rings f of nilpotency class c for all c  2and c,d for (c, d) ∈{(3, 3), (3, 2), (4, 2)}. We apply our computations to obtain information about p-adic, reduced, and topological zeta functions, in particular pertaining to their degrees and some special values. Keywords Graded ideal zeta functions · Free nilpotent Lie rings · Local functional equations Mathematics Subject Classification 17B70 · 11M41 · 11S40 1 Introduction 1.1 Enumerating graded ideals in graded Lie rings Let R be the ring of integers of a number field or the completion of such a ring at a nonzero prime ideal. Let L be a nilpotent R-Lie algebra of nilpotency class c, free of finite rank over c (i ) R, with lower central series (γ (L)) .For i ∈{1,..., c},set L := γ (L)/γ (L).The i i http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

Enumerating graded ideals in graded rings associated to free nilpotent Lie rings

Loading next page...
 
/lp/springer_journal/enumerating-graded-ideals-in-graded-rings-associated-to-free-nilpotent-6DzD6j9FK9
Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
0025-5874
eISSN
1432-1823
D.O.I.
10.1007/s00209-018-2062-9
Publisher site
See Article on Publisher Site

Abstract

Math. Z. https://doi.org/10.1007/s00209-018-2062-9 Mathematische Zeitschrift Enumerating graded ideals in graded rings associated to free nilpotent Lie rings 1 2 Seungjai Lee · Christopher Voll Received: 14 June 2016 / Accepted: 12 February 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract We compute the zeta functions enumerating graded ideals in the graded Lie rings associated with the free d-generator Lie rings f of nilpotency class c for all c  2and c,d for (c, d) ∈{(3, 3), (3, 2), (4, 2)}. We apply our computations to obtain information about p-adic, reduced, and topological zeta functions, in particular pertaining to their degrees and some special values. Keywords Graded ideal zeta functions · Free nilpotent Lie rings · Local functional equations Mathematics Subject Classification 17B70 · 11M41 · 11S40 1 Introduction 1.1 Enumerating graded ideals in graded Lie rings Let R be the ring of integers of a number field or the completion of such a ring at a nonzero prime ideal. Let L be a nilpotent R-Lie algebra of nilpotency class c, free of finite rank over c (i ) R, with lower central series (γ (L)) .For i ∈{1,..., c},set L := γ (L)/γ (L).The i i

Journal

Mathematische ZeitschriftSpringer Journals

Published: May 30, 2018

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off