Geodesic
Quotient rings, chain conditions and injective ring endomorphisms
Glasgow mathematical journal, Tome 31 (1989) no. 2, pp. 173-181

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

In this paper, the situation we shall be concerned with is that of a ring R, with a ring monomorphism α: R → R, which will not be assumed to be surjective.Much work has been done on the skew polynomial ring R[x, α] and the skew Laurent polynomial ring R[x, x-1, α], where α is an automorphism—see [3] for example. However, the fact that α is not surjective renders the study of these objects much more difficult. 
Wilkinson, J. C. Quotient rings, chain conditions and injective ring endomorphisms. Glasgow mathematical journal, Tome 31 (1989) no. 2, pp. 173-181. doi: 10.1017/S0017089500007709
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