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Finitely generated commutative semigroups

Published online by Cambridge University Press:  18 May 2009

D. B. McAlister  and
L. O'Carroll
D. B. McAlister
Affiliation:
Northern Illinois University, De Kalb, Illinois 60115, U.S.A.
L. O'Carroll
Affiliation:
Northern Illinois University, De Kalb, Illinois 60115, U.S.A.
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Since all the semigroups considered in this paper are commutative, we shall use the terms “semigroup” and “group” where we actually mean “commutative semigroup” and “commutative group”. Some basic results from the theory of semigroups are required and will be used without explicit mention; these results may be found in [1, § 4.3]. We shall denote the additive semigroups of integers, positive integers, negative integers, positive rationals by Z, Z+, Z-, Q+ respectively.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 11 , Issue 2 , July 1970 , pp. 134 - 151
Copyright
Copyright © Glasgow Mathematical Journal Trust 1970

References

REFERENCES

1.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Vol. I, Math. Surveys of the American Math. Soc. 7 (Providence, R.I., 1961).Google Scholar
2.Dubreil, P., Contribution a la theorie des demigroupes. Mem. Acad. Sci. Inst. France (2) 63, no. 3 (1941), 1–52.Google Scholar
3.Fuchs, L., Abelian groups (London, 1960).Google Scholar
4.Herstein, I. N., Topics in algebra (Waltham, Mass., 1964).Google Scholar
5.Levin, R. G., On commutative nonpotent archimedean semigroups, Pacific J. Math, 27 (1968), 365–371.CrossRefGoogle Scholar
6.McAlister, D. B., Characters on commutative semigroups, Quarterly J. Math. Oxford Ser. 2, 19 (1968) 141–157.CrossRefGoogle Scholar
7.Petrich, M., On the structure of a class of commutative semigroups, Czechoslovak Math. J. 14 (1964), 147–153.CrossRefGoogle Scholar
8.Redei, L., The theory of finitely generated commutative semigroups (London, 1965).Google Scholar
9.Tamura, T., Commutative nonpotent archimedean semigroup with cancellation law, Gakugei Tokoshima Univ. 8 (1957), 5–11.Google Scholar
10.Tamura, T., Notes on commutative archimedean semigroups, I, II, Proc. Japan Acad. 42 (1966) 35–40, 545–548.Google Scholar
11.Tamura, T., Construction of trees and commutative archimedean semigroups, Math. Nachr. 36 (1968), 257–287.CrossRefGoogle Scholar
12.Yamada, M., Construction of finite commutative z-semigroups, Proc. Japan Acad. 40 (1964), 94–98.Google Scholar