Basic Concepts and Notations

Yuqi Guo, Yun Liu and Shoufeng Wang
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Yuqi Guo: Lanzhou University, School of Mathematics and Statistics
Yun Liu: Yuxi Normal University, Department of Mathematics
Shoufeng Wang: Yunnan Normal University, Department of Mathematics

Chapter Chapter 1 in Topics on Combinatorial Semigroups, 2024, pp 1-26 from Springer

Abstract: Abstract In this preliminary chapter, we give a short account of some basic concepts and notations which will be used throughout the book. Section 1.1 contains the background knowledge in the general semigroup theory. Section 1.2 covers a short introduction to the theory of languages. In Sect. 1.3, we discuss dense subsets (languages) in semigroups. Dense subsets (languages) will play an important role throughout the book. In Sect. 1.4, we deal with a special but important class of words called primitive words which will be often used in the book. Some elementary properties of infinite words are involved in the last section.

Date: 2024
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DOI: 10.1007/978-981-99-9171-6_1

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