Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
DE
EN
Books
Journals
Events
Topic Page
Marketing
Log in
Learn more about individual access
Request company access
13th International Engine Congress 2026 | 24 + 25 February 2026

Meeting Place for the Powertrain and Sustainable Fuels Community

Take part as a speaker in the 13th International Engine Congress 2026, the Meeting Place for the Powertrain, and Sustainable Fuels Community for the exchange of experience. Submit a subject proposal online about our main subject areas: Passenger car engine technology, Commercial vehicle engine technology and Sustainable Fuels & Energy!
EXTENDED SEARCH
Log in
Top
Published in:
Read chapter Read first chapter

2024 | OriginalPaper | Chapter

11. A Contribution to the Study of a Class of Noncommutative Ideals Admitting Finite Gröbner Bases

Authors : Laila Mesmoudi, Yatma Diop

Published in: Mathematics of Computer Science, Cybersecurity and Artificial Intelligence

Publisher: Springer Nature Switzerland

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This chapter delves into the study of noncommutative ideals admitting finite Gröbner bases, building upon the classical Gröbner bases theory originated by Buchberger. It explores the extension of Gröbner bases to noncommutative polynomial rings, highlighting the loss of finiteness in this context. The authors generalize previous results, proving that any surjective homomorphism can replace the homomorphism used in earlier works. This generalization allows for a flexible approach to characterizing noncommutative ideals with finite Gröbner bases, offering a choice in their representation. The chapter is rich in mathematical detail, leveraging well-known properties and theorems to present a compelling argument. It concludes by emphasizing the practical implications of the findings, suggesting potential applications in various fields.
AI Generated

This summary of the content was generated with the help of AI.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter On S-Lifting Semimodules over Semirings
next chapter Construction of Numbers with the Same “Normality” Properties as a Given Number
Literature
1.
M. F. Atiyah, I. G. MacDonaldIntroduction to commutative algebra, University of Oxford
2.
G. M. BergmanThe diamond lemma for ring theory, Adv. Math. 29(1978), 178–218.
3.
B. BuchbergerBruno Buchberger’s PhD thesis 1965 : An algorithm for finding the basis elements of the residue class of a zero dimensional ideal, Journal of Symbolic Computation 41(2006) 475–511.
4.
D. Cox, J. Little, D. O’SheaIdeals, Varieties and Algorithms An Introduction to Computational Algebraic Geometry and Commutative Algebra. Second edition Springer, Undergraduate Texts in Mathematics 1997
5.
Y. DIOP, D. SOWOn finite noncommutative Gröbner bases, Algebra Colloquium 27:3 (2020) 381–388.
6.
D. Eisenbud, I. Peeva, B. SturmfelsNoncommutative Gröbner bases for commutative algebras, Proc. Amer. Math. Soc. 126(1998) 687–691
7.
N. JacobsonBasic Algebra I Second Edition, Library of Congress Cataloging in Publication Data
8.
T. MoraAn introduction to commutative and non-commutative Gröbner Bases, Journal of Theoretical Computer Science, 13(1994) 131–173
9.
R. B. MurrayFree associative algebras, non-commutative Gröbner bases, and universal associative envelopes for non-associative structures, CMUC: Comment. Math. Univ. Carolin. 55, 3(2014) 341–379
Metadata
Title
A Contribution to the Study of a Class of Noncommutative Ideals Admitting Finite Gröbner Bases
Authors
Laila Mesmoudi
Yatma Diop
Copyright Year
2024
Book
Mathematics of Computer Science, Cybersecurity and Artificial Intelligence

Print ISBN: 978-3-031-66221-8

Electronic ISBN: 978-3-031-66222-5

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-66222-5_11

Premium Partner

    Image Credits