Ultrasymmetry Of Valuations In Transcendental Valued Fields Extensions

Transcendental valued field extensions became an important, but also difficult, area of research lately, due to the complexity of the analysis and characterization of the extensions of their valuations, from K to K(X1,…,Xn), when the transcendental degree is larger than 1. One promising approach introduced the concept of symmetric extensions with respect to the indeterminates X1,…,Xn, that allowed having a closer look inside the structure of an extension of a valuation from K to K(X1,…,Xn). While these symmetric valuations have been analyzed up to a significant level of detail, a sub-class of them, namely the ultrasymmetric extensions are still an unexplored territory. This paper deals with the investigation of this domain of ultrasymmetric extensions, with the purpose of identifying their form and characteristics.