A signature-based algorithm for computing Gröbner-Shirshov bases in skew solvable polynomial rings

Xiangui Zhao; Yang Zhang

Open Mathematics (2015)

  • Volume: 13, Issue: 1
  • ISSN: 2391-5455

Abstract

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Signature-based algorithms are efficient algorithms for computing Gröbner-Shirshov bases in commutative polynomial rings, and some noncommutative rings. In this paper, we first define skew solvable polynomial rings, which are generalizations of solvable polynomial algebras and (skew) PBW extensions. Then we present a signature-based algorithm for computing Gröbner-Shirshov bases in skew solvable polynomial rings over fields.

How to cite

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Xiangui Zhao, and Yang Zhang. "A signature-based algorithm for computing Gröbner-Shirshov bases in skew solvable polynomial rings." Open Mathematics 13.1 (2015): null. <http://eudml.org/doc/270998>.

@article{XianguiZhao2015,
abstract = {Signature-based algorithms are efficient algorithms for computing Gröbner-Shirshov bases in commutative polynomial rings, and some noncommutative rings. In this paper, we first define skew solvable polynomial rings, which are generalizations of solvable polynomial algebras and (skew) PBW extensions. Then we present a signature-based algorithm for computing Gröbner-Shirshov bases in skew solvable polynomial rings over fields.},
author = {Xiangui Zhao, Yang Zhang},
journal = {Open Mathematics},
keywords = {Gröbner-Shirshov basis; Skew solvable polynomial ring; Signature-based algorithm},
language = {eng},
number = {1},
pages = {null},
title = {A signature-based algorithm for computing Gröbner-Shirshov bases in skew solvable polynomial rings},
url = {http://eudml.org/doc/270998},
volume = {13},
year = {2015},
}

TY - JOUR
AU - Xiangui Zhao
AU - Yang Zhang
TI - A signature-based algorithm for computing Gröbner-Shirshov bases in skew solvable polynomial rings
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - null
AB - Signature-based algorithms are efficient algorithms for computing Gröbner-Shirshov bases in commutative polynomial rings, and some noncommutative rings. In this paper, we first define skew solvable polynomial rings, which are generalizations of solvable polynomial algebras and (skew) PBW extensions. Then we present a signature-based algorithm for computing Gröbner-Shirshov bases in skew solvable polynomial rings over fields.
LA - eng
KW - Gröbner-Shirshov basis; Skew solvable polynomial ring; Signature-based algorithm
UR - http://eudml.org/doc/270998
ER -

References

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