Geodesic
Galois Theory of Essential Extensions of Modules
Canadian journal of mathematics, Tome 24 (1972) no. 4, pp. 573-579

Voir la notice de l'article provenant de la source Cambridge University Press

The purpose of this paper is to exploit an analogy between algebraic extensions of fields and essential extensions of modules, in which the role of the algebraic closure of a field F is played by the injective hull H(M) of a unitary left R-module M. (The notion of * ‘algebraic’ extensions of general algebraic systems has been studied by Shoda; see, for example [5].)In this analogy, the role of a polynomial p(x) is played by a homomorphism of R-modules (1) which will be called an ideal homomorphism into M. The process of solving the equation p(x) = 0 in F, or in an algebraic extension of F, will be replaced by the process of extending an ideal homomorphism (1) to a homomorphism F * from R into M, or into an essential extension of M. 
Wiegand, Sylvia. Galois Theory of Essential Extensions of Modules. Canadian journal of mathematics, Tome 24 (1972) no. 4, pp. 573-579. doi: 10.4153/CJM-1972-051-x
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