Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-24T22:28:09.992Z Has data issue: false hasContentIssue false
  • English
  • Français

Free products with amalgamation of commutative inverse semigroups

Published online by Cambridge University Press:  09 April 2009

Teruo Imaoka
Teruo Imaoka
Affiliation:
Department of Mathematics, Monash University Clayton, Victoria, Australia, 3168.
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.

A class of algebras A is said to have the strong amalgamation property if for any indexed set of algebras {Ai: i ∈ J} from A, each having an algebra U ∈ A as a subalgebra, there exist an algebra B ∈ A and monomorphisms φi: Ai → B (for each i ∈ J) such that (i) φi|U = φi| U for all i,j∈J, (ii) φi(Ai) ∩ φi(Aj) =φi(U) for atl i, j ∈ J with i ≠ j, where φi|U denotes the restriction of φi to U. Omitting condition (ii) gives us the definition of the weak amalgamation property.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 22 , Issue 2 , September 1976 , pp. 246 - 251
Copyright
Copyright © Australian Mathematical Society 1976

References

Clifford, A. H. and Preston, G. B. (1961, 1967), The Algebraic Theory of Semigroups (Math. Surveys, No. 7, Amer. Math. Soc., Providence, R. I. Vol. I, Vol. II).Google Scholar
Hall, T. E. (1975), ‘Free products with amalgamation of inverse semigroups’, J. Algebra (to appear).CrossRefGoogle Scholar
Jónsson, Bjarni (1965), ‘Extensions of relational structures’, The Theory of Models (Proceedings of the 1963 International Symposium at Berkeley, edited by Addison, J. W., Henkin, L. and Tarski, A., North Holland, Amsterdam), 146–157.Google Scholar
Preston, G. B. (1973), ‘Inverse semigroups: some open questions’, Proceedings of a symposium on inverse semigroups and their generalizations, Northern Illinois University, 122–139.Google Scholar