Surjective Stability of Dickson-Siegel-Eichler-Roy Elementary Orthogonal Group

Ambily Ambattu Asokan; Adriraj Talukdar

Surjective Stability of Dickson-Siegel-Eichler-Roy Elementary Orthogonal Group

Commutative Algebra 2026-06-29 v1

Authors: Ambily Ambattu Asokan , Adriraj Talukdar

Abstract

Let $R$ be a commutative Noetherian ring in which $2$ is invertible. We prove that a conjugate of Petrov's odd elementary unitary group is contained in the DSER elementary orthogonal group defined over projective modules. We also show a sufficient condition regarding the Witt index of the quadratic module with a hyperbolic summand $\mathbb{H}(P)$ which implies the surjective stability of DSER orthogonal ${\rm K}_1$

Keywords

elementary orthogonal group surjective stability Witt index K1 projective modules

Cite

@article{arxiv.2606.30086,
  title  = {Surjective Stability of Dickson-Siegel-Eichler-Roy Elementary Orthogonal Group},
  author = {Ambily Ambattu Asokan and Adriraj Talukdar},
  journal= {arXiv preprint arXiv:2606.30086},
  year   = {2026}
}

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9 pages