PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 38(52), pp. 69--82 (1985)
EMBEDDING SEMIGROUPS IN GROUPS: A GEOMETRICAL APPROACH
Sava Krsti\'cMatematicki institut SANU, Beograd, Yugoslavia
Abstract: A way to visualize Mal'cev quasi-identities is presented. As a consequence an analogy, expressed in a geometric language, is found between Mal'cev and Lambek quasi-identities. These are known to be of a special form which is called stable here; it is proved that certain geometrically characterized sets of stable quasi-identities axiomatize the class of embeddable semigroups. The results of Mal'cev and Lambek are obtained as corollaries. The method of diagrams, borrowed from group theory, enabled us to give a unified treatment which seems to be conceptually simpler than those previously employed.
Classification (MSC2000): 20M10, 20F32
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