Electronic Resource
Springer
Semigroup forum
61 (2000), S. 385-404
ISSN:
1432-2137
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
E S , of a monoid S and Ch. Wells studied the relationship between Leech coextensions and those studied in a general categorical setting by J. Beck. In this paper it is completed some of the Wells results and it is given a classification of the Leech coextensions. Specifically, Wells shows that a Leech coextension is a Beck coextension if its corresponding functor is "centralizing" (a generalization of abelian-valued). Our Theorem 1.1 provides a technical condition under which Beck coextensions are actually abelian. This technical condition implies other properties as well. Corollary 1.8 provides three natural conditions under any of which the conditions of 1.1 are satisfied. Also it is provided an example of a non-abelian Beck coextension. Table 1 shows the general classification and Table 2 shows the reduced set of possibilities when the semigroup is a regular monoid. Stronger results are provided for coextensions with S an inverse monoid, and for extensions of groups by monoids.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/PL00006037
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