Pham Ngoc Ánh: Prime factorization and remainders of polynomials in non-commuting variables

Abstract:

It is a join work with F. Mantese. One can assign to a polynomial of non-commuting variables a finite-dimensional module of remainders.
This remainder module is used to show that every polynomial with constant has a unique prime factorization up to a permutation of factors
and similarity. Two polynomials are similar iff the remainder modules are isomorphic iff the usual standard factor-modules are isomorphic.
Furthermore a polynomial with constant is irreducible iff the remainder module is simple. We discuss also consequences of these results
together with naturally arising questions.

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