Hostname: page-component-76fb5796d-22dnz Total loading time: 0 Render date: 2024-04-25T17:25:35.838Z Has data issue: false hasContentIssue false
  • English
  • Français

The Immersibility of a Semigroup into a Group

Published online by Cambridge University Press:  20 November 2018

J. Lambek
J. Lambek*
Affiliation:
McGill University
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 semigroup is a set of elements which is closed under an associative operation, usually called multiplication. When can a semigroup be embedded in a group, i.e., under what condition is it isomorphic to a subset of a group? A necessary condition for immersibility is clearly the so-called cancellation law:

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 3 , 1951 , pp. 34 - 43
Copyright
Copyright © Canadian Mathematical Society 1951

References

[1] Malcev, A., On the immersion of an algebraic ring into afield, Math. Ann., vol. 113 (1937), 687.Google Scholar
[2] Malcev, A., Über die Einbettung von assoziativen Systemen in Gruppen, Mat. Sbornik, vol. 6 (48) (1939), 331–336.Google Scholar
[3] Malcev, A., Über die Einbettung von assoziativen Systemen in Gruppen, II, Mat. Sbornik, vol, 8 (50) (1940), 251–264.Google Scholar
[4] Seifert, H. and Threlfall, W., Lehrbuch der Topologie (New York, 1947).Google Scholar