Hostname: page-component-77c89778f8-9q27g Total loading time: 0 Render date: 2024-07-16T18:20:04.369Z Has data issue: false hasContentIssue false
  • English
  • Français

Direct products of finite monogenic inverse semigroups

Published online by Cambridge University Press:  14 November 2011

D. C. Trueman
D. C. Trueman
Affiliation:
Monash University, Clayton, Victoria, Australia
Get access Rights & Permissions [Opens in a new window]

Synopsis

We characterize direct products of finite monogenic inverse semigroups; we show that a finite monogenic inverse semigroup which is not a group is directly indecomposable and that a finite semigroup which is decomposable into a direct product of monogenic inverse semigroups which are not groups is uniquely so decomposable. We determine when a finite semigroup can be decomposed into a direct product of non-group monogenic inverse semigroups and show how the direct factors, if they exist, can be found.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 92 , Issue 3-4 , 1982 , pp. 301 - 317
Copyright
Copyright © Royal Society of Edinburgh 1982

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Birkhoff, G.. Lattice Theory, 3rd edn. Amer. Math. Soc. Colloq. Publ. 25 (Providence, R.I.: A.M.S., 1967).Google Scholar
2Chang, C. C., Jónsson, B. and Tarski, A.. Refinement properties for relational structures. Fund. Math. 55 (1964), 249–281.CrossRefGoogle Scholar
3Clifford, A. H. and Preston, G. B.. The algebraic theory of semigroups. Amer. Math. Soc. Surveys 7/1 and II (1961 and 1967).CrossRefGoogle Scholar
4Djadčenko, G. G. and Šaǐn, B. M.. The structure of finite monogenic inverse semigroups. Ural. Gos. Univ. Mat. Zap. 9 (1974), 15–21.Google Scholar
5Eberhart, C. and Selden, J.. One-parameter inverse semigroups. Trans. Amer. Math. Soc. 168 (1972), 53–66.CrossRefGoogle Scholar
6Eršova, T. I.. Monogenically inverse semigroups. Ural. Gos. Univ. Mat. Zap. 8 (1971), 30–33.Google Scholar
7Gluskin, L. M.. Elementary generalized groups. Mat. Sb. 41 (1957), 23–36.Google Scholar
8Jónsson, B.. The unique factorization problem for finite relational structures. Colloq. Math. 14 (1966), 1–32.CrossRefGoogle Scholar
9Trueman, D. C.. Finite direct products of finite cyclic semigroups and their characterization. Proc. Roy. Soc. Edinburgh Sect. A 85 (1980), 337–351.CrossRefGoogle Scholar
10Trueman, D. C.. Direct products of cyclic semigroups. In Semigroups, pp. 103–110, ed. Hall, T. E., Jones, P. R. and Preston, G. B. (New York: Academic Press 1980).CrossRefGoogle Scholar