Skip to main content Accessibility help
×
Home

On the lattice of varieties of completely regular semigroups

  • P. R. Jones (a1)

Abstract

Several morphisms of this lattice V(CR) are found, leading to decompostions of it, and various sublattices, into subdirect products of interval sublattices. For example the map V → V ∪ G (where G is the variety of groups) is shown to be a retraction of V(CR); from modularity of the lattice V(BG) of varieties of bands of groups it follows that the map V → (V ∪ V V G) is an isomorphism of V(BG).

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      On the lattice of varieties of completely regular semigroups
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      On the lattice of varieties of completely regular semigroups
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      On the lattice of varieties of completely regular semigroups
      Available formats
      ×

Copyright

References

Hide All
[1]Birjukov, A. P., ‘Varieties of idempotent semigroups’, Algebra i Logika 9 (1970), 255273.
[2]Fennemore, C. F., ‘All varieties of bands,’ Math. Nachr. 48 (1971), I: 237252, II: 253–262.
[3]Gerhard, J. A., ‘The lattice of equational classes of idempotent semigroups,’ J. Algebra 15 (1970), 195224.
[4]Gützer, G., General lattice theory (Birkhauser Verlag, Basel, 1978).
[5]Hall, T. E., ‘On regular semigroups,’ J. Algebra 24 (1973), 124.
[6]Hall, T. E. and Jones, P. R., ‘On the lattice of varieties of bands of groups,’, Pacific J. Math. 91 (1980) 327337.
[7]Howie, J. M., An introduction to semigroup theory (Academic Press, London, 1976).
[8]Jones, P. R., ‘Completely simple semigroups: free products, free semigroups and varieties’, Proc. Royal Soc. Edinburgh A 88 (1981), 293313.
[9]Masevickii, C. I., ‘On identities in varieties of completely simple semigroups over abelian groups’, Contemporary algebra, Leningrad (1978), pp. 8189 (Russian).
[10]Neumann, H., Varieties of groups (Springer-Verlag, New York, 1967).
[11]Petrich, M., ‘Certain varieties and quasivarieties of completely regular semigroups,’ Canad. J. Math. 29 (1977), 11711197.
[12]Petrich, M., ‘On the varieties of completely regular semigroups,’ Semigroup Forum 25 (1982), 153170.
[13]Petrich, M. and Reilly, N. R., ‘Varieties of groups and of completely simple semigroups,’ Bull. Austral. Math. Soc. 23 (1981), 339359.
[14]Petrich, M. and Reilly, N. R., ‘Near varieties of idempotent generated completely simple semigroups,’ Algebra Universalis, to appear.
[15]Petrich, M. and Reilly, N. R., “All variables of central simple semigroups”, Trans. Amer. Math. Soc., tp appear.
[16]Petrich, M. and Reilly, N. R., “Certain homomorphisms of the lattice of varieties of completely simple semigroups,’ J. Austral. Math. Soc., to appear.
[17]Rasin, V. V., ‘On the lattice of varieties of completely simple semigroups’, Semigroup Forum 17 (1979), 113122.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

MSC classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed