Notes on commutative power joined semigroups
Richard G. Levin, Takayuki Tamura · Pacific Journal of Mathematics · 1970
Let S be a commutative semigroup.The main theorem in this paper is to prove that the following two conditions are equivalent: (1) For all α, be S there are positive integers m, n such that a m = b\ (2) For all α, b e S, a 1 = a m b n , b r = & 8 α* for some I, m, n, r, s, t.As a consequence of the theorem, the authors prove that a commutative archimedean semigroup S without idempotent is power joined if and only if the structure group of S is a torsion group.Math. 27 (1968), 365-371. 5. Takayuki Tamura, Note on unipotent ίnversible semigroups, Kodai Math.Sem.Reports (1954), 93-95.6., Commutative nonpotent archimedean semigroups with cancellation law 1, J. of Gakugei, Tokushima Univ.8 (1951), 5-11.7., Construction of trees and commutative archimedean semigroups, Math.Nachr.