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On the existence of nonsingular bilinear forms on projective modules

In: Tatra Mountains Mathematical Publications, vol. 32, no. 3
Marzena Ciemała - Kazimierz Szymiczek
Detaily:
Rok, strany: 2005, 1 - 13
O článku:
We prove that in a domain $R$ an ideal of $R$ admits a nonsingular bilinear form if and only if its square is a principal ideal. We also show that the isometry classes of bilinear forms on an ideal correspond bijectively to the square classes of the group of units of $R$. When $R$ is one-dimensional noetherian domain, each finitely generated projective $R$-module is isomorphic to $M = I oplus Rn$ and it admits a nonsingular bilinear form if and only if $I2$ is a principal ideal. When $R$ is Dedekind domain of characteristic not two in which $2$ is not a unit, we show that for each invertible nonprincipal ideal $I$ the direct sum $M = I oplus I-1$ admits a nonsingular bilinear form $β$ which makes $M$ into an indecomposable inner product space.
Ako citovať:
ISO 690:
Ciemała, M., Szymiczek, K. 2005. On the existence of nonsingular bilinear forms on projective modules. In Tatra Mountains Mathematical Publications, vol. 32, no.3, pp. 1-13. 1210-3195.

APA:
Ciemała, M., Szymiczek, K. (2005). On the existence of nonsingular bilinear forms on projective modules. Tatra Mountains Mathematical Publications, 32(3), 1-13. 1210-3195.