Geodesic
Central extensions in Mal'tsev varieties
Theory and applications of categories, Tome 7 (2000), pp. 219-226

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

We show that every algebraically-central extension in a Mal'tsev variety - that is, every surjective homomorphism $f : A \longrightarrow B$ whose kernel-congruence is contained in the centre of $A$, as defined using the theory of commutators - is also a central extension in the sense of categorical Galois theory; this was previously known only for varieties of $\Omega$-groups, while its converse is easily seen to hold for any congruence-modular variety.

Classification : 08B05, 08C05, 18G50.
Keywords: 
@article{TAC_2000_7_a9,
     author = {G. Janelidze and G.M. Kelly},
     title = {Central extensions in {Mal'tsev} varieties},
     journal = {Theory and applications of categories},
     pages = {219--226},
     publisher = {mathdoc},
     volume = {7},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2000_7_a9/}
}
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G. Janelidze; G.M. Kelly. Central extensions in Mal'tsev varieties. Theory and applications of categories, Tome 7 (2000), pp. 219-226. http://geodesic.mathdoc.fr/item/TAC_2000_7_a9/