2022/03/01 by Labib Haddad, Haddad, Labib
Computer Science · Mathematics · #05E14 #06M99 #11B99 #20M99 #Advanced Algebra and Logic #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05E14 #msc:06M99 #msc:11B99 #msc:20M99 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2203.01119
12 pages, French and English versions
arxiv created 2022/03/01 · openalex publication_date 2022/03/01 · arxiv updated 2022/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a notably simpler and shorter proof of H. B. Neumann's result which is stated, cursorly, like this. For any well-ordered subset, A, of a totally ordered semigroup, the set of products of any finite number of elements of A is itself well-ordered. Moreover, for each t, there are only a finite number of such products equal to t.