A generalization of Dumas-Eisenstein criterion

We introduce an interesting and rather large class of monoid homomorphisms, on arbitrary integral domain R, that we call Dumas valuations. Then we formulate a conjecture addressing the question asking when a polynomial f∈ R[X] cannot be written as a product $f = gh$ for some nonconstant polynomials g, h ∈ R[X]. The statement of the conjecture presents a significant generalization of the classical Eisenstein-Dumas irreducibility criterion. In particular our approach can be very useful while studying the irreducibility problem for multivariate polynomials over any integral domain. We provide a strong evidence that our conjecture should be true.