A proof of a version of Hensel’s lemma

https://doi.org/10.5281/zenodo.5728221

• Dinamérico P. Pombo Jr. Instituto de Matemática e Estatı́stica Universidade Federal Fluminense https://orcid.org/0000-0002-9516-4459

Keywords: local rings, discrete valuation rings, Hensel’s lemma

Abstract

By using a few basic facts, a proof of a known version of Hensel’s lemma in the context of local rings is presented.

References

E. Artin. Algebraic Numbers and Algebraic Functions, American Mathematical Society, Providence, Rhode Island, 2005.

N. Bourbaki. Commutative Algebra, Hermann and Addison-Wesley, Paris and Reading, Massachusetts, 1972.

J.W. Cassels. Local Fields, London Mathematical Society Student Texts 3, Cambridge University Press, Cambridge, 1986.

R. Godement. Cours d’algbre, Troisime dition, Enseignement des Sciences, Hermann, Paris, 1966.

N. Koblitz. p-adic Numbers, p-adic Analysis, and Zeta-Functions, Second edition, Springer-Verlag, Berlin. Heidelberg. New York, 1984.

J. P. Serre. Corps Locaux, Quatrime dition, Actualits Scientifiques et Industrielles 1296, Hermann, Paris, 1968.

J. P. Serre. A Course in Arithmetic, Third printing, Graduate Texts in Mathematics 7, Springer-Verlag, Berlin. Heidelberg. New York, 1985.