The embeddability of a semigroup—Conditions common to Mal’cev and Lambek
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- by George C. Bush PDF
- Trans. Amer. Math. Soc. 157 (1971), 437-448 Request permission
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
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G. C. Bush, On embedding a semigroup in a group, Ph.D. Thesis, Queen’s University, Kingston, Ontario, 1961.
- 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 H. Jackson, The embedding of a semigroup in a group, M.A. Thesis, Queen’s University, Kingston, Ontario, 1956.
- J. Lambek, The immersibility of a semigroup into a group, Canad. J. Math. 3 (1951), 34–43. MR 38991, DOI 10.4153/cjm-1951-005-8
- 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
- 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
Additional Information
- © Copyright 1971 American Mathematical Society
- 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