1. See e. g. O. Schmidt. The Abstract Theory of Groups (in Russian). Kiev 1916, p. 58.
2. This can be proved in the same way as the theorem is proved that every commutative ring without divisors of 0 can be immersed into a field (i. e. considering “quotients”a/b). See B. L. v. d. Waerden. Moderne Algebra Berlin 1930, Bd. I, S. 47–48.
3. A. Suschkewitsch, Über die Erweiterung der Semigruppe bis zur ganzen Gruppe. Commun. Soc. Math. Kharkoff et Inst. Sci. de Math. et Mécan. Univ. Kharkoff (4)12 (1935), 81–86 (in Russian).
4. See e.g. v. d. Waerden, op. cit.Moderne Algebra. Berlin 1930, Bd. I, S. 49.