Standard

Gröbner-Shirshov bases method for Gelfand-Dorfman-Novikov algebras. / Bokut, L. A.; Chen, Yuqun; Zhang, Zerui.

In: Journal of Algebra and its Applications, Vol. 16, No. 1, 1750001, 01.01.2017.

Research output: Contribution to journal › Article › peer-review

Harvard

Bokut, LA, Chen, Y & Zhang, Z 2017, 'Gröbner-Shirshov bases method for Gelfand-Dorfman-Novikov algebras', Journal of Algebra and its Applications, vol. 16, no. 1, 1750001. https://doi.org/10.1142/S0219498817500013

APA

Bokut, L. A., Chen, Y., & Zhang, Z. (2017). Gröbner-Shirshov bases method for Gelfand-Dorfman-Novikov algebras. Journal of Algebra and its Applications, 16(1), [1750001]. https://doi.org/10.1142/S0219498817500013

Vancouver

Bokut LA, Chen Y, Zhang Z. Gröbner-Shirshov bases method for Gelfand-Dorfman-Novikov algebras. Journal of Algebra and its Applications. 2017 Jan 1;16(1):1750001. doi: 10.1142/S0219498817500013

Author

Bokut, L. A. ; Chen, Yuqun ; Zhang, Zerui. / Gröbner-Shirshov bases method for Gelfand-Dorfman-Novikov algebras. In: Journal of Algebra and its Applications. 2017 ; Vol. 16, No. 1.

BibTeX

@article{2113a109913a4c409bdcedce069d61ab,
title = "Gr{\"o}bner-Shirshov bases method for Gelfand-Dorfman-Novikov algebras",
abstract = "We establish Gr{\"o}bner-Shirshov base theory for Gelfand-Dorfman-Novikov algebras over a field of characteristic 0. As applications, a PBW type theorem in Shirshov form is given and we provide an algorithm for solving the word problem of Gelfand-Dorfman-Novikov algebras with finite homogeneous relations. We also construct a subalgebra of one generated free Gelfand-Dorfman-Novikov algebra which is not free.",
keywords = "commutative differential algebra, Gelfand-Dorfman-Novikov algebra, Gr{\"o}bner-Shirshov basis, word problem, LIE-ALGEBRAS, MODULES, CALCULUS, HAMILTONIAN OPERATORS, CHARACTERISTIC-0, Grobner-Shirshov basis",
author = "Bokut, {L. A.} and Yuqun Chen and Zerui Zhang",
year = "2017",
month = jan,
day = "1",
doi = "10.1142/S0219498817500013",
language = "English",
volume = "16",
journal = "Journal of Algebra and its Applications",
issn = "0219-4988",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "1",

}

RIS

TY - JOUR

T1 - Gröbner-Shirshov bases method for Gelfand-Dorfman-Novikov algebras

AU - Bokut, L. A.

AU - Chen, Yuqun

AU - Zhang, Zerui

PY - 2017/1/1

Y1 - 2017/1/1

N2 - We establish Gröbner-Shirshov base theory for Gelfand-Dorfman-Novikov algebras over a field of characteristic 0. As applications, a PBW type theorem in Shirshov form is given and we provide an algorithm for solving the word problem of Gelfand-Dorfman-Novikov algebras with finite homogeneous relations. We also construct a subalgebra of one generated free Gelfand-Dorfman-Novikov algebra which is not free.

AB - We establish Gröbner-Shirshov base theory for Gelfand-Dorfman-Novikov algebras over a field of characteristic 0. As applications, a PBW type theorem in Shirshov form is given and we provide an algorithm for solving the word problem of Gelfand-Dorfman-Novikov algebras with finite homogeneous relations. We also construct a subalgebra of one generated free Gelfand-Dorfman-Novikov algebra which is not free.

KW - commutative differential algebra

KW - Gelfand-Dorfman-Novikov algebra

KW - Gröbner-Shirshov basis

KW - word problem

KW - LIE-ALGEBRAS

KW - MODULES

KW - CALCULUS

KW - HAMILTONIAN OPERATORS

KW - CHARACTERISTIC-0

KW - Grobner-Shirshov basis

UR - http://www.scopus.com/inward/record.url?scp=84955565473&partnerID=8YFLogxK

U2 - 10.1142/S0219498817500013

DO - 10.1142/S0219498817500013

M3 - Article

AN - SCOPUS:84955565473

VL - 16

JO - Journal of Algebra and its Applications

JF - Journal of Algebra and its Applications

SN - 0219-4988

IS - 1

M1 - 1750001

ER -

ID: 8975150