Types of linkage of quadratic Pfister forms

Given a field F of positive characteristic p, theta is an element of H-p(n-1)(F) and beta,gamma is an element of Fx, we prove that if the symbols theta <^> d beta/beta and theta <^> d gamma/gamma in H-p(n)(F) share the same factors in H-p(1) (F) then the symbol theta <^> d beta/beta <^>d gamma/gamma in H-p(n+1)(F) is trivial. We conclude that when p = 2, every two totally separably (n - 1)-linked n-fold quadratic Pfister forms are inseparably (n - 1)-linked. We also describe how to construct non-isomorphic n-fold Pfister forms which are totally separably (or inseparably) (n - 1)-linked, i.e. share all common (n 1)-fold quadratic (or bilinear) Pfister factors. (C) 2018 Elsevier Inc. All rights reserved.