Geodesic
On the Brauer Group of Algebras Having a Grading and an Action
Canadian journal of mathematics, Tome 28 (1976) no. 3, pp. 533-552

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

Beginning with Wall's introduction [19] of Z2-graded central simple algebras over a field K, a number of related generalizations of the Brauer group have been proposed. In [16] the field K was replaced by a commutative ring R, building upon the theory developed in [1]. The concept of a G-graded central simple K-algebra (G an abelian group) was first defined in [12]; this work and that of [16] was subsequently unified in [6] and [7] via the construction and computation of the graded Brauer group Bφ{R, G) (φ a bilinear form from G X G to U(R), the units of R). 
Orzech, Morris. On the Brauer Group of Algebras Having a Grading and an Action. Canadian journal of mathematics, Tome 28 (1976) no. 3, pp. 533-552. doi: 10.4153/CJM-1976-053-6
@article{10_4153_CJM_1976_053_6,
     author = {Orzech, Morris},
     title = {On the {Brauer} {Group} of {Algebras} {Having} a {Grading} and an {Action}},
     journal = {Canadian journal of mathematics},
     pages = {533--552},
     year = {1976},
     volume = {28},
     number = {3},
     doi = {10.4153/CJM-1976-053-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1976-053-6/}
}
TY  - JOUR
AU  - Orzech, Morris
TI  - On the Brauer Group of Algebras Having a Grading and an Action
JO  - Canadian journal of mathematics
PY  - 1976
SP  - 533
EP  - 552
VL  - 28
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1976-053-6/
DO  - 10.4153/CJM-1976-053-6
ID  - 10_4153_CJM_1976_053_6
ER  - 
%0 Journal Article
%A Orzech, Morris
%T On the Brauer Group of Algebras Having a Grading and an Action
%J Canadian journal of mathematics
%D 1976
%P 533-552
%V 28
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1976-053-6/
%R 10.4153/CJM-1976-053-6
%F 10_4153_CJM_1976_053_6

[1] 1. Auslander, M. and Goldman, O., The Brauer group of a commutative ring, Trans. Amer. Math. Soc. 97 (1960), 367–409. Google Scholar

[2] 2. Bass, H., Lectures on topics in algebraic K-theory, Tata Institute for Fundamental Research, Bombay, 1967. Google Scholar

[3] 3. Bass, H., Algebraic K-theory (Benjamin, W. A., New York, 1968). Google Scholar

[4] 4. Cartan, H. and Eilenberg, S., Homologuai algebra (Princeton University Press, 1956). Google Scholar

[5] 5. Chase, S. U., Harrison, D. K. and Rosenberg, A., Galois theory and Galois cohomology of commutative rings, Memoirs Amer. Math. Soc. 52 (1965), 1–19. Google Scholar

[6] 6. Childs, L. N., The Brauer group of graded algebras II: graded Galois extensions, Trans. Amer. Math. Soc. 201+ (1975), 137–160. Google Scholar

[7] 7. Childs, L. N., Garfinkel, G. and Orzech, M., The Brauer group of graded Azumaya algebras, Trans. Amer. Math. Soc. 175 (1973), 299–326. Google Scholar

[8] 8. Frohlich, A. and Wall, C. T. C., Generalizations of the Brauer group, to appear. Google Scholar

[9] 9. Harada, M., Some criteria for hereditarily of crossed products, Osaka J. Math. 1 (1964), 69–80. Google Scholar

[10] 10. Harrison, D. K., Abelian extensions of commutative rings, Memoirs Amer. Math. Soc. 52 (1965), 66–79. Google Scholar

[11] 11. Janusz, G. J., Separable algebras over commutative rings, Trans. Amer. Math. Soc. 122 (1966), 461–479. Google Scholar

[12] 12. Knus, M.-A., Algebras graded by a group, Category Theory, Homology Theory and their Applications, Battelle Inst. Conf. Seattle, Wash., 1968, vol. II (Springer, Berlin, 1969). Google Scholar

[13] 13. Long, F. W., A generalization of the Brauer group of graded algebras, Proc. London Math. Soc. (3) 29 (1974), 237–256. Google Scholar

[14] 14. Long, F. W., The Brauer group of dimodule algebras, J. Algebra 30 (1974), 559–601. Google Scholar

[15] 15. Orzech, M. and Small, C., The Brauer group of commutative rings, Lecture Notes in Pure and Applied Mathematics, No. 11 (Marcel Dekker, New York, 1975). Google Scholar

[16] 16. Small, C., The Brauer-Wall group of a commutative ring, Trans. Amer. Math. Soc. 156 (1971), 455–491. Google Scholar

[17] 17. Sweedler, M. E., Hopf algebras (Benjamin, W. A., New York, 1969). Google Scholar

[18] 18. Van, B. L. der Waerden, Modern algebra, vol. II (Ungar, New York, 1950). Google Scholar

[19] 19. Wall, C. T. C., Graded Brauer groups, J. Reine Angew. Math. 213 (1964), 187–199. Google Scholar

[20] 20. Yamazaki, K., On projective representations and ring extensions of finite groups, J. Fac. Science, Univ. of Tokyo 10 (1964), 147–195. Google Scholar

Cité par Sources :