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- W2000993917 abstract "Suppose $D$ is a Dedekind domain of characteristic 2 and $(M,varphi )$ is an inner product space, i.e. $M$ is a finitely generated projective $D$ module supplied with a nonsingular symmetric bilinear form $varphi$. It is shown that $(M,varphi )$ is determined up to isometry by the extension of $varphi$ to $F{ otimes _D}M$, where $F$ is the quotient field of $D$, and the value module ${mathcal Q}(M)$ of all $varphi (m,m)$ for $m$ in $M$. In particular, a hyperbolic space ${mathbf {H}}(M)$ is completely determined by the rank of the finitely generated projective module $M$. As consequences, genera coincide with isometry classes, and if ${N_1}$ and ${N_2}$ are isometric nonsingular submodules of $(M,varphi )$ such that ${mathcal Q}({N_1}^ bot ) = {mathcal Q}({N_2}^ bot )$, then ${N_1}^ bot$ and ${N_2}^ bot$ are isometric. Also, given an $F$ inner product space $(V,varphi )$ and a ${D^{(2)}}$ submodule $P$ of $D$, a necessary and sufficient condition is given for the existence of a $D$ inner product space $(M,Psi )$ such that $(FM,Psi ) cong (V,varphi )$ and ${mathcal Q}(M) = P$." @default.
- W2000993917 created "2016-06-24" @default.
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- W2000993917 date "1985-01-01" @default.
- W2000993917 modified "2023-09-26" @default.
- W2000993917 title "On inner product spaces over Dedekind domains of characteristic two" @default.
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- W2000993917 doi "https://doi.org/10.1090/s0002-9939-1985-0766516-5" @default.
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