This is a description of some different approaches which have been taken to the problem of generalizing the algebraic closure of a field. Work surveyed is by Enoch and Hochster (commutative algebra), Raphael (categories and rings of quotients), Borho (the polynomial approach), and Carson (logic).
Later work and applications are given.
@article{urn:eudml:doc:41759,
title = {On algebraic closures.},
journal = {Publicacions Matem\`atiques},
volume = {36},
year = {1992},
pages = {913-923},
mrnumber = {MR1210026},
zbl = {0780.12002},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41759}
}
Raphael, R. On algebraic closures.. Publicacions Matemàtiques, Tome 36 (1992) pp. 913-923. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41759/