Hostname: page-component-848d4c4894-8kt4b Total loading time: 0 Render date: 2024-06-22T18:46:19.404Z Has data issue: false hasContentIssue false
  • English
  • Français

Commutative semigroup varieties with the amalgamation property

Part of: Varieties Semigroups

Published online by Cambridge University Press:  09 April 2009

G. T. Clarke
G. T. Clarke
Affiliation:
Monash University, Clayton, Victoria 3168, Australia
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.

We determine which varieties of commutative semigroups have the weak or strong amalgamation property. These are precisely the varieties of inflations of semilattices of abelian groups.

MSC classification

Secondary: 20M07: Varieties and pseudovarieties of semigroups 08B25: Products, amalgamated products, and other kinds of limits and colimits
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 30 , Issue 3 , February 1981 , pp. 278 - 283
Copyright
Copyright © Australian Mathematical Society 1981

References

Clarke, G. T. (1980), ‘On completely regular semigroup varieties and the amalgamation property’, Semigroups, Monash University, Australia, edited by Hall, T. E., Jones, P. R. and Preston, G. B., pp. 159–165 (Academic Press, New York).CrossRefGoogle Scholar
Clifford, A. H. and Preston, G. B. (1961), Algebraic theory of semigroups, Volume I (Math. Surveys 7, Amer. Math. Soc., Providence, R.I.).CrossRefGoogle Scholar
Evans, T. (1971), ‘The lattice of semigroup varieties’, Semigroup Forum 2, 1–43.CrossRefGoogle Scholar
Hall, T. E. (1978a), ‘Inverse semigroup varieties with the amalgamation property’, Semigroup Forum 16, 37–51.CrossRefGoogle Scholar
Hall, T. E. (1978b), ‘Representation extension and amalgamation for semigroups’, Quart. J. Math. Oxford Ser. 29, 309–334.CrossRefGoogle Scholar
Hall, T. E. (1979), ‘Inverse and regular semigroups and amalgamation’, Algebra Paper 39, Monash University, Melbourne.CrossRefGoogle Scholar
Howie, J. M. (1968), ‘Commutative semigroup amalgams’, J. Austral. Math. Soc. 8, 609–630.CrossRefGoogle Scholar
Imaoka, T. (1976a), ‘Free products with amalgamation of bands’, Mem. Fac. Lit. Sci. Shimane Univ. Natur. Sci. 10, 7–17.Google Scholar
Imaoka, T. (1976b), ‘Free products with amalgamation of commutative inverse semigroups’, J. Austral. Math. Soc. Ser. A 22, 246–251.CrossRefGoogle Scholar
Kimura, N. (1957), On semigroups (Ph.D. Thesis, The Tulane University of Louisiana).Google Scholar
Sin-Min, L. (1976), ‘Lattice of equational subclasses of distributive semigroups’, Nanta Math. 9, 65–69.Google Scholar
Petrich, M. (1974), ‘All subvarieties of a certain variety of semigroups’, Semigroup Forum 7, 104–152.CrossRefGoogle Scholar
Tamura, T. (1969), ‘Semigroups satisfying identity xy = f(x, y)’, Pacific J. Math. 31, 513–521.CrossRefGoogle Scholar