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/