Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-15T10:32:25.120Z Has data issue: false hasContentIssue false

The join of the varieties of strict inverse Semigroups and rectangular bands

Published online by Cambridge University Press:  18 May 2009

Mario Petrich
Affiliation:
Simon Fraser University, Burnaby, B.C., Canada.
Norman R. Reilly
Affiliation:
Simon Fraser University, Burnaby, B.C., Canada.
Rights & Permissions [Opens in a new window]

Extract

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.

In recent years, certain varieties of semigroups with unary operations (of “inversion”) have received considerable attention. Generally speaking, these have been contained in one or other of the two classes of completely regular semigroups (that is, semigroups that are unions of groups) and inverse semigroups. For instances of the former see [1], [2], [3], [6], [10], [14] and [15], and for instances of the latter see [7], [8], [12] and [13].

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1984

References

REFERENCES

1.Clifford, A. H., The free completely regular semigroup on a set, J. Algebra 59 (1979), 434451.CrossRefGoogle Scholar
2.Gerhard, J. A., Free completely regular semigroups I, J. Algebra, to appear.Google Scholar
3.Hall, T. E. and Jones, P. R., On the lattice of varieties of bands of groups, Pacific J. Math. 91 (1980), 327337.CrossRefGoogle Scholar
4.Hoehnke, H.-J., Über direkte Produkte vollständig einfacher Halbgruppen, Monatsb. Deutsch. Akad. Wiss. Berlin 4 (1962), 695698.Google Scholar
5.Howie, J. M., An introduction to semigroup theory (Academic Press, 1976).Google Scholar
6.Jones, P. R., Completely simple semigroups: free products, free semigroups and varieties, Proc. Roy. Soc. Edinburgh Sect. A 88 (1981), 293313.CrossRefGoogle Scholar
7.Kleiman, E. I., On the lattice of varieties of inverse semigroups, Izv. Vyss. Ucebn. Zaved. Matematica 7 (1976), 106109 (Russian).Google Scholar
8.Kleiman, E. I., On bases of identities of Brandt semigroups, Semigroup Forum 13 (1977), 209218.CrossRefGoogle Scholar
9.Lallement, G., Demi-groupes réguliers, Ann. Mat. Pura Appl. (4) 77 (1967), 47129.CrossRefGoogle Scholar
10.Petrich, M., Certain varieties and quasivarieties of completely regular semigroups, Canad. J. Math. 29 (1977), 11711197.CrossRefGoogle Scholar
11.Petrich, M., Structure of regular semigroups (Cahiers Math. Montpellier, 1977).Google Scholar
12.Reilly, N. R., Varieties of completely semisimple inverse semigroups, J. Algebra 65 (1980), 427444.CrossRefGoogle Scholar
13.Reilly, N. R., Modular sublattices of the lattice of varieties of inverse semigroups, Pacific J. Math. 89 (1980), 405517.CrossRefGoogle Scholar
14.Rasin, V. V., On the lattice of varieties of completely simple semigroups, Semigroup Forum 17 (1979), 113122.CrossRefGoogle Scholar
15.Rasin, V. V., On the varieties of Cliffordian semigroups, Semigroup Forum 23 (1981), 201220.CrossRefGoogle Scholar
16.Yamada, M., Regular semigroups whose idempotents satisfy permutation identities, Pacific J. Math. 21 (1967), 371392.CrossRefGoogle Scholar
17.Yamada, M., Generalized Brandt semigroups, Mem. Fac. Lit. Sci. Shimane Univ. Natur. Sci. No. 3 (1970), 18.Google Scholar