JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (4): 54-57.doi: 10.6040/j.issn.1671-9352.0.2019.253

Previous Articles    

Generalized inverse via Gröbner-Shirshov basis

Gulshadam Yunus, Abdukadir Obul*   

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, Xinjiang, China
  • Published:2020-04-09

PDF (PC)

421

Abstract: By using Gröbner-Shirshov basis theory for associative algebra, the generalized inverse of the element 1-ba in a ring with identity is computed in terms of the given generalized inverse of the element 1-ab.

Key words: ring, Grö, bner-Shirshov basis, composition, generalized inverse

CLC Number: 

  • O153.3
[1] BARNES B A. Common operator properties of the linear operators RS and SR[J]. Proc Amer Soc, 1998, 126(4):1055-1061.
[2] BUCHBERGER B. An algorithm for finding a basis for the residue class ring of a zero-dimensional ideal[D]. Innsbruck: University of Innsbruck, 1965.
[3] SHIRSHOV A I. Some algorithmic problem for Lie algebras[J]. Sibirsk Mat Z, 1962, 3(2):292-296.
[4] BERGMAN G M. The diamond lemma for ring theory[J]. Adv in Math, 1978, 29:178-218.
[5] HERFORT W. A Gröbner-Shirshov basis approach tu Huas identity[J]. Beitr Algebra Geom, 2014, 55:387-391.
[6] ZHAO X H. Jacobsons lemma via Gröbner-Shirshov basis[J]. Algebra Colloquium, 2017, 24(2):300-314.
[7] BOKUT L A, CHEN Y Q. Gröbner-Shirshov basis and their calculation[J]. Bulletin of Mathematical Sciences, 2014, 4(3):325-395.
[1] CHEN Li-xue, YIN Xiao-bin. α-Skew quasi nil Armendariz rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(4): 41-47.
[2] . [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(3): 51-57.
[3] WEN Liu-ying, YUAN Wei. Clustering method for multi-label symbolic value partition [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(3): 58-69.
[4] TANG Yi-ming, ZHANG Zheng, LU Qi-ming. Gaussian kernel fuzzy C-means clustering driven by piecewise quadratic transfer function [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(3): 107-112.
[5] ZHANG Min-qing, ZHOU Neng, LIU Meng-meng, WANG Han, KE Yan. Reversible data hiding in homomorphic encrypted domain based on Paillier [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(3): 1-8.
[6] XU Ying-ying, YIN Xiao-bin. On JGR-clean rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(2): 84-90.
[7] XU Xiu-juan, YAN Shuo, ZHU Ye-qing. Global regularity for very weak solutions to non-homogeneous A-harmonic equation [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(2): 48-56.
[8] SUN Xiao-qing, XIAO Yan-ting, CUI ran-ran. Discussions on the Q-cleanness of rings and Q-clean corner [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(2): 79-83.
[9] YANG Liu, MA Jing. Armendariz property for a group ring over the Hamiltons quaternion ring [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(1): 1-4.
[10] Yun-miao GUI,Zhong WU,Hong-chun HU. Pricing strategy of vehicles and cargos matching platform in the sharing economy [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(1): 69-76,85.
[11] ZHANG Wei-jie, WANG Xin-li, WANG Han-jie. Uniqueness of differential polynomials of meromorphic functions IM sharing a value [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(8): 90-96.
[12] DUAN Ran. Counting solutions of a binary quadratic congruence equation [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(8): 108-120.
[13] CHEN Yi-ning, QIN Long. Strongly g(x)-nil-clean rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(6): 41-46.
[14] CHEN Xun, HUANG Qiong-xiang, CHEN Lin. Interval edge-coloring of the generalized θ-chain [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(6): 59-70.
[15] XIONG Ya-ping, CAI Jian-sheng. The classification of f-coloring of random graphs [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(6): 71-74.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd