4 citations · 8 across the 8 of their papers we have counts for
13 papers
An elementary proof of the Artin--Springer theorem for generalized quadratic forms over quaternion algebras
Amir Hossein Nokhodkar
We give a short and simple proof that an anisotropic generalized quadratic form over a quaternion division algebra with involution of the first kind, in arbitrary characteristic, r…
Sharp Bounds on Diminished Sombor Index
Meysam Taheri-Dehkordi, Amir Hossein Nokhodkar, Gholam Hossein Fath-Tabar
The Diminished Sombor index of a simple graph is a recently introduced degree-based topological index, defined as \[ DSO(G)= \sum_{uv\in E(G)} \frac{\sqrt{d_u^2+d_v^2}}…
Quadratic descent of hermitian forms (with an erratum)
Amir Hossein Nokhodkar
Quadratic descent of hermitian and skew hermitian forms over division algebras with involution of the first kind in arbitrary characteristic is investigated and a criterion, in ter…
Quadratic -forms with applications to hermitian forms
Amir Hossein Nokhodkar
We study some properties of quadratic forms with values in a field whose underlying vector spaces are endowed with the structure of right vector spaces over a division ring extensi…
Separable extensions of orthogonal involutions in characteristic two
Amir Hossein Nokhodkar
It is shown that an anisotropic orthogonal involution in characteristic two is totally decomposable if it is totally decomposable over a separable extension of the ground field. In…
Orthogonal involutions and totally singular quadratic forms in characteristic two
A. -H. Nokhodkar
We associate to every central simple algebra with involution of orthogonal type in characteristic two a totally singular quadratic form which reflects certain anisotropy properties…
Symmetric square-central elements in products of orthogonal involutions in characteristic two
Amir Hossein Nokhodkar
We obtain some criteria for a symmetric square-central element of a totally decomposable algebra with orthogonal involution in characteristic two, to be contained in an invariant q…
Pfister involutions in characteristic two
A. -H. Nokhodkar
In characteristic two, it is shown that a central simple algebra of degree equal to a power of two with anisotropic orthogonal involution is totally decomposable, if it becomes eit…
Quadratic descent of totally decomposable orthogonal involutions in characteristic two
Amir Hossein Nokhodkar
We investigate the quadratic descent of totally decomposable algebras with involution of orthogonal type in characteristic two. Both separable and inseparable extensions are includ…
On the decomposition of metabolic involutions
Amir Hossein Nokhodkar
The problem of whether a metabolic idempotent of a central simple algebra with involution is contained in an invariant quaternion subalgebra is investigated. As an application, the…
Applications of the Wall form to unipotent isometries of index two
Amir Hossein Nokhodkar
We investigate the Wall form of unipotent elements of index two in the orthogonal group and obtain a decomposition for these elements. Also, in characteristic two, the relation bet…
On biquaternion algebras with involution of orthogonal type
A. -H. Nokhodkar
We investigate the pfaffians of decomposable biquaternion algebras with involution of orthogonal type. In characteristic two, a classification of these algebras in terms of their p…
On totally decomposable algebras with involution in characteristic two
M. G. Mahmoudi, A. -H. Nokhodkar
A necessary and sufficient condition for a central simple algebra with involution over a field of characteristic two to be decomposable as a tensor product of quaternion algebras w…