let r be a ring and v be a matrix valuation on r. it is shown that, there exists a correspondence between matrix valuations on r and some special subsets ?(mvpr) of the set of all square matrices over r, analogous to the correspondence between invariant valuation rings and abelian valuation functions on a division ring. furthermore, based on malcolmson’s localization, an alternative proof for t...

The reduced anisotropic unitary Whitehead groups of henselian division algebras with involutions are computed in the cases where centers residue special types.

The process of residue division has certain interesting properties and quite possibly has applications in respect to special problems. Unfortunately, the residue division process is not a substitute for normal division. It appears that the only way in which division can be effected in the residue code is by the utilization of techniques similar to those employed for division in a consistently w...

This special issue on ‘American Empire in Global History’ is the result of a joint-research project at History Division, Institute for Open and Transdisciplinary Research Initiatives...

Let R be a ring and V be a matrix valuation on R. It is shown that, there exists a correspondence between matrix valuations on R and some special subsets ?(MVPR) of the set of all square matrices over R, analogous to the correspondence between invariant valuation rings and abelian valuation functions on a division ring. Furthermore, based on Malcolmson’s localization, an alternative proof for t...