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Transactions of the American Mathematical Society

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The embeddability of a semigroup--Conditions common to Mal'cev and Lambek


Author: George C. Bush
Journal: Trans. Amer. Math. Soc. 157 (1971), 437-448
MSC: Primary 20.93
DOI: https://doi.org/10.1090/S0002-9947-1971-0281814-4
MathSciNet review: 0281814
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Abstract: Two systems of conditions--due to Mal'cev and to Lambek--are known to be necessary and sufficient for a semigroup to be embeddable in a group. This paper shows by means of an example that the conditions common to the two systems are not sufficient to guarantee embeddability.


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

  • [1] G. C. Bush, On embedding a semigroup in a group, Ph.D. Thesis, Queen's University, Kingston, Ontario, 1961.
  • [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
  • [3] H. Jackson, The embedding of a semigroup in a group, M.A. Thesis, Queen's University, Kingston, Ontario, 1956.
  • [4] J. Lambek, The immersibility of a semigroup into a group, Canadian J. Math. 3 (1951), 34–43. MR 0038991
  • [5] A. Malcev, Über die Einbettung von assoziativen Systemen in Gruppen, Rec. Math. [Mat. Sbornik] N.S. 6 (48) (1939), 331–336 (Russian, with German summary). MR 0002152
  • [6] A. Malcev, Über die Einbettung von assoziativen Systemen in Gruppen. II, Rec. Math. [Mat. Sbornik] N.S. 8 (50) (1940), 251–264 (Russian, with German summary). MR 0002895

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0281814-4
Keywords: Embeddability of a semigroup, Mal'cev conditions, Lambek conditions, lunar conditions, half-edge equations, polyhedral conditions, nonembeddable semigroup
Article copyright: © Copyright 1971 American Mathematical Society