Geodesic
Signatures and Semi Signatures of Abstract Witt Rings and Witt Rings of Semilocal Rings
Canadian journal of mathematics, Tome 30 (1978) no. 4, pp. 872-895

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

This paper originated in an attempt to carry over the results of [3] from the case of a field of characteristic different from two to that of semilocal rings. To carry this out, we reverse the point of view of [3] and do assume a full knowledge of the theory of Witt rings of classes of nondegenerate symmetric bilinear forms over semilocal rings as given, for example, in [10; 11]. It turns out that the rings WT of [3] are just the residue class rings of W(C), the Witt ring of a semilocal ring C, modulo certain intersections of prime ideals. 
Kleinstein, Jerrold L.; Rosenberg, Alex. Signatures and Semi Signatures of Abstract Witt Rings and Witt Rings of Semilocal Rings. Canadian journal of mathematics, Tome 30 (1978) no. 4, pp. 872-895. doi: 10.4153/CJM-1978-076-1
@article{10_4153_CJM_1978_076_1,
     author = {Kleinstein, Jerrold L. and Rosenberg, Alex},
     title = {Signatures and {Semi} {Signatures} of {Abstract} {Witt} {Rings} and {Witt} {Rings} of {Semilocal} {Rings}},
     journal = {Canadian journal of mathematics},
     pages = {872--895},
     year = {1978},
     volume = {30},
     number = {4},
     doi = {10.4153/CJM-1978-076-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1978-076-1/}
}
TY  - JOUR
AU  - Kleinstein, Jerrold L.
AU  - Rosenberg, Alex
TI  - Signatures and Semi Signatures of Abstract Witt Rings and Witt Rings of Semilocal Rings
JO  - Canadian journal of mathematics
PY  - 1978
SP  - 872
EP  - 895
VL  - 30
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1978-076-1/
DO  - 10.4153/CJM-1978-076-1
ID  - 10_4153_CJM_1978_076_1
ER  - 
%0 Journal Article
%A Kleinstein, Jerrold L.
%A Rosenberg, Alex
%T Signatures and Semi Signatures of Abstract Witt Rings and Witt Rings of Semilocal Rings
%J Canadian journal of mathematics
%D 1978
%P 872-895
%V 30
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1978-076-1/
%R 10.4153/CJM-1978-076-1
%F 10_4153_CJM_1978_076_1

[1] 1. Beaza, R., Quadratische Formen iiber semilokalen Ringen, Habilitationschrift, Saarbrucken (1975). Google Scholar

[2] 2. Baeza, R. and Knebusch, M., Annulatoren von Pfisterformen iiber semilokalen Ringen, Math. Z. 140 (1974), 41–62. Google Scholar

[3] 3. Becker, E. and E. Kôpping, Reduzierte quadratische Formen und Semiordnungen reeler Korper, Abh. Math. Sem. Hamburg 46 (1977), 143–177. Google Scholar

[4] 4. Elman, R., Lam, T. Y., and Prestel, A., On some Hasse principles over formally real fields, Math. Z. 134 (1973), 291–301. Google Scholar

[5] 5. Knebusch, M., Isometrien iiber semilokalen Ringen, Math. Z. 108 (1969), 255–268. Google Scholar

[6] 6. Knebusch, M., Grothendieck-und Wittringe von nichtausgearteten symmetrischen Bilinearjormen, Sitzber. Heidelberg Akad. Wiss. (1969/70), 93–157. Google Scholar

[7] 7. Knebusch, M., Runde Formen iiber semilokalen Ringen, Math. Ann. 193 (1971), 21–34. Google Scholar

[8] 8. Knebusch, M., Generalization of a theorem of Artin-Pfister, J. of Alg. 36 (1975), 46–67. Google Scholar

[9] 9. Knebusch, M., Remarks on the paper “Equivalent topological properties of the space of signatures of a semilocal ring” by Rosenberg, A. and Ware, R., Pub. Math. 24 (1977), 181–188. Google Scholar

[10] 10. Knebusch, M., Rosenberg, A., and Ware, R., Structure of Witt rings and quotients of abelian group rings, Amer. J. Math. 94 (1972), 119–155. Google Scholar

[11] 11. Knebusch, M., Rosenberg, A., and Ware, R., Signatures on semilocal rings, J. of Alg. 26 (1973), 208–250. Google Scholar

[12] 12. Milnor, J. and Husemoller, D., Symmetric bilinear forms, Ergeb. d. Math. 73 (Springer Verlag, New York-Heidelberg-Berlin, 1973). Google Scholar

[13] 13. Prestel, A., Lectures on formally real fields, Instituto de Matemâtica Pura e Aplicada, Brasilia, 1975. Google Scholar

[14] 14. Roy, A., Cancellation of quadratic forms over commutative rings, J. of Alg. 10 (1968), 286–298. Google Scholar

[15] 15. Rosenberg, A. and Ware, R., Equivalent topological properties of the space of signatures of a semilocal ring, Pub. Math. 23 (1976), 283–289. Google Scholar

Cité par Sources :