Relative determinant of a bilinear module

• Autorzy: Przemysław Koprowski
• Języki publikacji: EN

Abstrakty

EN

The aim of the paper is to generalize the (ultra-classical) notion of the determinant of a bilinear form to the class of bilinear forms on projective modules without assuming that the determinant bundle of the module is free. Successively it is proved that this new definition preserves the basic properties, one expects from the determinant. As an example application, it is shown that the introduced tools can be used to significantly simplify the proof of a recent result by B. Rothkegel.

Słowa kluczowe

EN

determinant; bilinear forms; projective modules

Kategorie tematyczne

• 11E39: Bilinear and Hermitian forms
• 15A63: Quadratic and bilinear forms, inner products \SeeMainly{}
• 13C10: Projective and free modules and ideals

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2014
• Tom: 34
• Numer: 2
• Strony: 203-212

Twórcy

autor

Przemysław Koprowski

• Faculty of Mathematics, University of Silesia, ul. Bankowa 14, 40-007 Katowice, Poland

Bibliografia

• [1] M. Ciemała and K. Szymiczek, On the existence of nonsingular bilinear forms on projective modules, Tatra Mt. Math. Publ. 32 (2005) 1-13.
• [2] O. Goldman, Determinants in projective modules, Nagoya Math. J. 18 (1961) 27-36.
• [3] M.A. Marshall, Bilinear forms and orderings on commutative rings, volume~71 of Queen's Papers in Pure and Applied Mathematics (Queen's University, Kingston, ON, 1985).
• [4] J. Milnor and D. Husemoller, Symmetric bilinear forms (Springer-Verlag, New York, 1973).
• [5] H.P. Petersson, Polar decompositions of quaternion algebras over arbitrary rings, preprint, 2008. http://www.fernuni-hagen.de/petersson/download/polar-quat-l.pdf
• [6] B. Rothkegel, Nonsingular bilinear forms on direct sums of ideals, Math. Slovaca 63(4) (2013) 707-724. doi: 10.2478/s12175-013-0130-5.
• [7] C.A. Weibel, The K-book. An introduction to algebraic K-theory. volume 145 of Graduate Studies in Mathematics (American Mathematical Society, Providence, 2013).

Identyfikatory

DOI

10.7151/dmgaa.1221