Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-23T23:13:13.011Z Has data issue: false hasContentIssue false

Verbal varieties of inverse semigroups

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

Ross Wilkinson
Affiliation:
Department of Mathematics Monash UniversityClayton, Victoria, Australia3168
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.

A verbal product is introduced for a particular class of varieties of inverse semigroups and this product is shown to be associative. As well, the structure of this class is examined.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Bales, J., ‘On product varieties of inverse semigroups’ (Algebra Paper 31, Department of Mathematics, Monash University, 1978).Google Scholar
[2]Birkhoff, G., ‘On the structures of abstract algebras’, Proc. Cambridge Philos. Soc. 31 (1935), 433454.Google Scholar
[3]Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Vol. I. (Amer. Math. Soc. Math. Surveys 7, Providence, R.I., 1961).Google Scholar
[4]Djadchenko, G. G., ‘On identities in monogenic inverse semigroups’, Algebra and Theory of Numbers, Kabardino-Balkarsk Gos. Univ. Učen. Zap. (Nalcik), 2 (1977), 5777, (Russian).Google Scholar
[5]Green, D., ‘The lattice of congruences on an inverse semigroups’, Pacific J. Math. 57 (1975), 141152.CrossRefGoogle Scholar
[6]Howie, J. M., An introduction to semigroup theory, (Academic Press, London, 1976).Google Scholar
[7]Kleinmann, E. I., ‘On basis of identities of Brandt semigroups’, Semigroup Forum 13 (1977), 209218.CrossRefGoogle Scholar
[8]Kurosh, A. G., The theory of groups, 2nd ed. 1953, (Translation in English by Hirsch, K. A., Chelsea, 1956).Google Scholar
[9]Mal'cev, A. I., ‘Multiplication of classes of algebraic systems’, Siberian Math. J. 8 (1967), 254267.Google Scholar
[10]Moran, S., ‘Associative operations on groups I’, Proc. London Math. Soc. 6 (1956), 581596.CrossRefGoogle Scholar
[11]Neumann, B. H., ‘Identical relations in groups I’, Math. Ann. 114 (1937), 506525.CrossRefGoogle Scholar
[12]Neumann, H., Varieties of groups, (Ergebnisse der Mathematik und ihre Grenzgebiete, 37, Springer-Verlag, Berlin, 1967).CrossRefGoogle Scholar
[13]Reilly, N. R., Varieties of inverse semigroups, Proceedings of the Conference on Semigroups in Honour of Alfred H. Clifford, pp. 8593, Tulane University, New Orleans 1979.Google Scholar