Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Amalgamated products of semigroups: the embedding problem

Author: Gérard Lallement
Journal: Trans. Amer. Math. Soc. 206 (1975), 375-394
MSC: Primary 20M10
MathSciNet review: 0364505
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A necessary and sufficient condition for a semigroup amalgam to be embeddable is given. It is in the form of a countable set of equational implications with existential quantifiers. Furthermore it is shown that no finite set of equational implications can serve as a necessary and sufficient condition. Howie's sufficient condition (see [5]) is derived as a consequence of our main theorem.

References [Enhancements On Off] (What's this?)

  • [1] N. Bourbaki, Eléments de mathématique, Algèbre, Chaps. 1-3, Hermann, Paris, 1970. MR 43 #2.
  • [2] A. H. Clifford and G. B. Preston, The algebraic theory of semigroups. Vol. II, Mathematical Surveys, No. 7, American Mathematical Society, Providence, R.I., 1967. MR 0218472 (36 #1558)
  • [3] P. A. Grillet and Mario Petrich, Free products of semigroups amalgamating an ideal, J. London Math. Soc. (2) 2 (1970), 389–392. MR 0276385 (43 #2132)
  • [4] T. E. Hall, Inverse semigroups and the amalgamation property (to appear).
  • [5] J. M. Howie, Embedding theorems with amalgamation for semigroups, Proc. London Math. Soc. (3) 12 (1962), 511–534. MR 0138696 (25 #2139)
  • [6] E. S. Ljapin, Intersections of independent subsemigroups of a semigroup, Izv. Vysš. Učebn. Zaved. Matematika 1970 (1970), no. 4 (95), 67–73 (Russian). MR 0281812 (43 #7526)
  • [7] A. I. Malcev, On the immersion of associative systems in groups, Mat. Sb. 6 (1939), 331-336. (Russian) MR 2, 7.
  • [8] -, On the immersion of associative systems in groups. II, Mat. Sb. 8 (1940), 251-264. (Russian) MR 2, 128.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 20M10

Retrieve articles in all journals with MSC: 20M10

Additional Information

PII: S 0002-9947(1975)0364505-4
Keywords: Semigroup amalgam, amalgamated products of semigroups, embedding of amalgams, free products of semigroups
Article copyright: © Copyright 1975 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia