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
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Isomorphisms of Four Dimensional Perfect Non-simple Evolution Algebras Read chapter Read first chapter

2020 | OriginalPaper | Chapter

Semi-ring Based Gröbner–Shirshov Bases over a Noetherian Valuation Ring

Authors : Yatma Diop, Laila Mesmoudi, Djiby Sow

Published in: Associative and Non-Associative Algebras and Applications

Publisher: Springer International Publishing

Log in

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

search-config
loading …

Abstract

Commutative and non commutative Gröbner–Shirshov bases were first studied over fields and after extended to some particular rings. In theses works, the monomials are in a monoid. Recently, Bokut and al. gave a new extension of Gröbner–Shirshov bases over a field by choosing the monomials in a semi-ring rather in a monoid. In this paper, we study Gröbner–Shirshov bases where the monomials are in a semi-ring and the coefficients are in a noetherian valuation ring and we establish the relation between weak and strong Gröbner bases.

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 Primary Group Rings
next chapter The 4-Rank of the Class Group of Some Real Pure Quartic Number Fields
Literature
1.
2.
3.
4.
Bucherger, B.: An algorithm for finding the basis elements of the residue class of a zero dimensional ideal. J. Symb. Comput. 41, 475–511 (2006)
5.
Hironaka, H.: Resolution of singularities of an algebraic variety over a field of characteristic zero: I. Ann. Math. 79(1), 109–203 (1964)MathSciNetCrossRef
6.
Kandri-Rody, A., Kapur, D.: Computing a Gröbner basis of a polynomial ideal over a Euclidean domain. J. Symb. Comput. 7, 37–57 (1988)CrossRef
7.
Kapur, D., Yongyang, C.: An algorithm for computing a Gröbner basis of a polynomial ideal over a ring with zero divisors. Math. Comput. Sci., 601-634 (2009)MathSciNetCrossRef
8.
Mikhalev, A.A.: A composition lemma and the word problem for color Lie superalgebras. Moscow Univ. Math. Bull. 44(5), 87–90 (1989)
9.
Möller, H.M.: The construction of Gröbner bases using syzygies. J. Symb. Comput. 6, 345–359 (1988)CrossRef
10.
Mora, T.: An introduction to commutative and non-commutative Gröbner Bases. J. Theor. Comput. Sci. 13, 131–173 (1994)CrossRef
11.
12.
Shirshov, A.I.: On free Lie rings. Mat. Sb. (N.S.) 45(87):2, 113–122 (1958)
13.
14.
Yengui, I.: Constructive Commutative Algebra. Lecture Notes in Mathematics, vol. 2138. Springer series 304 (2015)MATH
15.
16.
17.
Yengui, I.: Corrigendum to “Dynamical Gröbner bases”. J. Algebra 301, 447–458 (2006) and to “Dynamical Grobener bases over Dedekind rings”. J. Algebra 324, 12–24 (2010), J. of Algebra 339, 370–375 (2011)
Metadata
Title
Semi-ring Based Gröbner–Shirshov Bases over a Noetherian Valuation Ring
Authors
Yatma Diop
Laila Mesmoudi
Djiby Sow
Copyright Year
2020
Book
Associative and Non-Associative Algebras and Applications

Print ISBN: 978-3-030-35255-4

Electronic ISBN: 978-3-030-35256-1

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-35256-1_11

Premium Partner

    Image Credits