Free operated monoids and Rewriting systems
Xing Gao, Jin Zhang
TL;DR
This paper introduces a rewriting systems approach to construct bases for quotients of free operated monoids, providing a unified method applicable to free -monoids and free groups.
Contribution
It offers a novel, unified rewriting-based method for constructing bases of quotients in free operated monoids, including free -monoids and free groups.
Findings
Unified approach to construct bases for quotients
Application to free -monoids and free groups
Effective method for capturing sections
Abstract
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.
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