Semigroup Forum

, Volume 97, Issue 3, pp 435–456 | Cite as

Free operated monoids and rewriting systems

  • Jin Zhang
  • Xing GaoEmail author


The construction of bases for quotients is an important problem. In this paper, applying the method of rewriting systems, we give a unified approach to construct sections—an alternative name for bases in semigroup theory—for quotients of free operated monoids. As applications, we capture sections of free \(*\)-monoids and free groups, respectively.


Operated monoids Term-rewriting systems Free \(*\)-monoids Free groups 



The authors are supported by the National Natural Science Foundation of China (No. 11771191), the Fundamental Research Funds for the Central Universities (No. lzujbky-2017-162), and the Natural Science Foundation of Gansu Province (Grant No. 17JR5RA175) and Shandong Province (No. ZR2016AM02). We thank the anonymous referee for valuable suggestions helping to improve the paper.


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Authors and Affiliations

  1. 1.School of Mathematics and StatisticsLanzhou UniversityLanzhouPeople’s Republic of China
  2. 2.School of Mathematics and Statistics, Key Laboratory of Applied Mathematics and Complex SystemsLanzhou UniversityLanzhouPeople’s Republic of China

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