Artículos de revistas
Sur Le Groupe Des Extensions Cycliques
Registro en:
Journal Of Algebra. , v. 63, n. 1, p. 268 - 278, 1980.
218693
10.1016/0021-8693(80)90036-8
2-s2.0-0039502414
Autor
Micali A.
Paques A.
Institución
Resumen
In this paper we give an explicit and elementary construction of the group of all cyclic extensions of prime degree of a given ring. We give explicit calculations in some particular cases. In the second part, under certains hypotheses concerning the base ring, we give a cohomological interpretation of this group. Next, the crucial question of the existence of primitive element for the algebra extensions of the vase ring is treated and finally, we examine certains cases where primitive elements always exists. © 1980. 63 1 268 278 Auslander, Goldman, The Brauer group of a commutative ring (1960) Transactions of the American Mathematical Society, 97, pp. 367-409 Azumaya, On maximally central algebras (1951) Nagoya Math. J., 2, pp. 119-150 Bourbaki, (1964) Algèbre Commutative, , Hermann, Paris, Chap. 5 Chase, Harrison, Rosenberg, Galois theory and cohomology of commutative rings (1965) Mem. Amer. Math. Soc., 52, pp. 15-33 Childs, The group of unramified Kummer extensions of prime degree (1977) Proceedings of the London Mathematical Society, 35, pp. 407-422 Harrison, Abelian extensions of commutative rings (1965) Mem. Amer. Math. Soc., 52, pp. 1-14 Knus, Ojanguren, Théorie de la descente et algèbres d'Azumaya (1974) Lecture Notes in Mathematics No. 389, , Springer-Verlag, Berlin/New York Micali, Villamayor, Sur les algèbres de Clifford, II (1970) J. Reine Angew. Math., 242, pp. 61-90 Micali, Revoy, Modules quadratiques (1977) Cahiers Mathématiques n∘ 10, , Université de Montpellier II, Montpellier Nakajima, On a group of cyclic extensions over commutative rings (1972) Math. J. Okayama Univ., 16, pp. 163-172 Raynaud, Anneaux locaux henséliens (1960) Lecture Notes in Mathematics No. 169, , Springer-Verlag, Berlin/New York Wang, Separable Algebras and Free Cubic Extensions Over Commutative Rings (1975) Ph. D. thesis, , Cornell University Weiss, (1963) Algebraic Number Theory, , McGraw-Hill, New York