Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-24T23:01:36.488Z Has data issue: false hasContentIssue false
  • English
  • Français

N-Semigroups and their translation semigroups

Published online by Cambridge University Press:  09 April 2009

Takayuki Tamura
Takayuki Tamura
Affiliation:
University of California, Davis, California, USA 95616
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

If h is a homomorphism of an N-semigroup onto an N-semigroup S′, then h induces a homomorphism h of the translation semigroup Λ(S) of S into Λ(S′) of S′. We will study the relations between the structures of S, S′ and Λ(S), Λ(S)′, and will introduce the specialized concepts of N-semigroups S. In particular, we will be interested in power-joined steady or endless N-semigroups. Finally, we will consider admissibility of torsion abelian groups, that is, consider what torsion abelian group can be a structure group of a power-joined steady N-semigroup.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 24 , Issue 2 , September 1977 , pp. 184 - 202
Copyright
Copyright © Australian Mathematical Society 1977

References

Chrislock, J. L. (1966), The Structure of Archimedean Semigroups, Dissertation, University of California, Davis, California.Google Scholar
Chrislock, J. L. (1969), “On medial semigroups”, J. Algebra 12, 1–9.CrossRefGoogle Scholar
Clifford, A. H. (1954), “Naturally totally ordered commutative semigroups”, Amer. J. Math. 76, 631–646.CrossRefGoogle Scholar
Clifford, A. H. and Preston, G. B. (1961), The Algebraic Theory of Semigroups, Vol. 1, Math Surveys, No. 7 (Amer. Math. Soc, Providence, R.I.).Google Scholar
Dickinson, R. P. (1970), Right Zero Union of Semigroups, Dissertation, University of California, Davis, California.Google Scholar
Fuchs, L. (1963), Partially Ordered Algebraic Systems, Pergamon Press, Oxford.Google Scholar
Gratzer, G. (1968), Universal Algebra, Van Nostrand, Princeton, New Jersey.Google Scholar
Hall, R. E. (1969), The Structure of Certain Commutative Separative and Commutative Cancellative Semigroups, Dissertation, Pennsylvania State University, Middletown, Pennsylvania.Google Scholar
Hall, R. E. (1972), “The translational hull of an N-semigroup”, Pac. J. Math. 41, 379–389.CrossRefGoogle Scholar
Higgins, J. C. (1969), “Representing N-semigroups”, Bull. Austral. Math. Soc. 115–125.CrossRefGoogle Scholar
Higgins, J. C. (1969a), “A faithful canonical representation for finitely generated N-semigroups”, Czech. Math. J. 19, 375–379.CrossRefGoogle Scholar
Kimura, N. (1958), “The structure of idempotent semigroups I”, Pac. J. Math. 8, 257–275.CrossRefGoogle Scholar
Kobayashi, Y. (1973), “Homomorphisms on N-semigroups into R + and the structure of N-semigroups”, J. Math. Tokushima University 7, 1–20.Google Scholar
Petrich, M. (1973), “Normal bands of commutative cancellative semigroups”, Duke Math. J. 40, 17–32.CrossRefGoogle Scholar
Petrich, M. (1973a), Introduction to Semigroups, C. E. Merril Publishing Co., Columbus, Ohio.Google Scholar
Rotman, J. J. (1965), The Theory of Groups (Allyn and Bacon Inc., Boston).Google Scholar
Sasaki, M. and Tamura, T. (1971), “Positive rational semigroups and commutative power-joined cancellative semigroups without idempotent”, Czech. Math. J. 21, 567–576.CrossRefGoogle Scholar
Tamura, T. (1957), “Commutative nonpotent archimedean semigroups with cancellation law I”, J. Gakugei Tokushima University 8, 5–11.Google Scholar
Tamura, T. (1970), “Abelian groups and N-semigroups”, Proc. Japan Acad. 46, 212–216.Google Scholar
Tamura, T. (1973), “Finitely generated steady N-semigroups”, Proc. Amer. Math. Soc. 41, 425–430.Google Scholar
Tamura, T. (1973a), “N-congruences of N-semigroups”, J. Algebra 27, 11–30.CrossRefGoogle Scholar
Tamura, T. (1974), “Irreducible N-semigroups”, Math. Nachr. 63, 71–78.CrossRefGoogle Scholar
Tamura, T. (1974a), “Basic study of N-semigroups and their homomorphisms”, Semigroup Forum 8, 21–50.CrossRefGoogle Scholar
Tamura, T. (1975), “Basic study of N-semigroups and their homomorphisms II”, Semigroup Forum 10, 250–261.CrossRefGoogle Scholar
Yamada, M. (1962), The Structure of Separative Bands, Dissertation, University of Utah, Salt Lake City, Utah.Google Scholar