Amalgamated products of semigroups: the embedding problem
HTML articles powered by AMS MathViewer
- by Gérard Lallement PDF
- Trans. Amer. Math. Soc. 206 (1975), 375-394 Request permission
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
-
N. Bourbaki, Eléments de mathématique, Algèbre, Chaps. 1-3, Hermann, Paris, 1970. MR 43 #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
- P. A. Grillet and Mario Petrich, Free products of semigroups amalgamating an ideal, J. London Math. Soc. (2) 2 (1970), 389–392. MR 276385, DOI 10.1112/jlms/2.Part_{3}.389 T. E. Hall, Inverse semigroups and the amalgamation property (to appear).
- J. M. Howie, Embedding theorems with amalgamation for semigroups, Proc. London Math. Soc. (3) 12 (1962), 511–534. MR 138696, DOI 10.1112/plms/s3-12.1.511
- 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 A. I. Malcev, On the immersion of associative systems in groups, Mat. Sb. 6 (1939), 331-336. (Russian) MR 2, 7. —, On the immersion of associative systems in groups. II, Mat. Sb. 8 (1940), 251-264. (Russian) MR 2, 128.
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 206 (1975), 375-394
- MSC: Primary 20M10
- DOI: https://doi.org/10.1090/S0002-9947-1975-0364505-4
- MathSciNet review: 0364505