Quadratic forms and quadrics of space over local rings

被引:0
作者
O. A. Starikova
机构
[1] North-Eastern State University, Magadan
基金
俄罗斯基础研究基金会;
关键词
Quadratic Form; Projective Space; Local Ring; Maximal Ideal; Projective Transformation;
D O I
10.1007/s10958-012-1061-3
中图分类号
学科分类号
摘要
Relatively recent and new results on the enumeration of classes of projective congruent quadrics and classes of projective equivalent quadrics of projective spaces over a local ring R = 2R with nilpotent principal maximal ideal are reflected in the paper. For the case of the basic ring R with nonprincipal maximal ideal, the enumerations of quadrics of projective plane are given up to projective equivalence. © 2012 Springer Science+Business Media New York.
引用
收藏
页码:177 / 186
页数:9
相关论文
共 16 条
[1]  
Artin E., Geometric Algebra, (1959)
[2]  
Benz W., Vorlesungen über Geometrie der Algebren, (1973)
[3]  
Cao Y., Szechtman F., Congruence of symmetric matrices over local rings, Linear Algebra Appl., 431, 9, pp. 1687-1690, (2009)
[4]  
Egorychev G.P., Zima E.V., Simple formulae for the number of quadrics and symmetric forms of modules over local rings, Commun. Algebra, 36, pp. 1426-1436, (2008)
[5]  
Kula M., Fields and quadratic form schemes, Ann. Math. Sil., 1, 13, pp. 7-22, (1985)
[6]  
Kula M., Counting Witt rings, J. Algebra, 206, 2, pp. 568-587, (1998)
[7]  
Levchuk V.M., Starikova O.A., Quadratic forms of projective spaces over rings, Mat. Sb., 197, 6, pp. 97-110, (2006)
[8]  
Levchuk V.M., Starikova O.A., A normal form and schemes of quadratic forms, J. Math. Sci., 152, 4, pp. 558-570, (2008)
[9]  
Marshall M., The elementary type conjecture in quadratic form theory, Algebraic and Arithmetic Theory of Quadratic Forms. Proc. of the Int. Conf., Univ. de Talca, Talca and Pucón, Chile, December 11-18, 2002, Contemp. Math., 344, pp. 275-293, (2004)
[10]  
O'Meara O.T., Lectures on Linear Groups, (1973)