key polynomials 2henselization 1limit key polynomials 1MacLane theory 1order type 1rational function fields 1regular complete sequences 1transcendental extensions 1valuation extensions 1valued fields 1
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math.AC2026
Common extensions of valuations to rational function fields
Arpan Dutta, Wael Mahboub
The paper characterizes which K‑conjugates of a minimal pair define monomial valuations that extend a given valuation on a rational function field, and introduces regular limit key…
math.AC2026
Finite Generation in Polynomial Semirings
Mohammad El Asal, Wael Mahboub
We study the semiring as an additive monoid where is a positive real algebraic number. In the atomic case, the atoms of are precisely the…