Leírás
Abstract: In this talk I present the joint work with F. Mantese. To every not necessarily commutative polynomial $\lambda$, i.e, to every element of a free algebra we associate a finite-dimensional representation which plays the role of the remainder module. This representation depends only on the polynomial $\lambda$ itself, not on a $\lambda$ containing free algebra and is easily to computed. In the case of polynomials with constant these representations encode companion structures like factorizations, similarity class, primary decomposition etc. The main result states that a polynomial with constant is irreducible iff the module of remainders is simple and two such polynomials are similar iff their modules of remainders are isomorphic. Moreover, factorizations of a polynomial with constant correspond uniquely composition chains. In the case of polynomials of one variable one obtains in this manner the classical theory because the variable itself is up to a scalar the unique irreducible polynomial without constant. We discuss applications and limitation of our method to polynomials without constant. For example, the module of remainders of any irreducible polynomial without constant in at least two variables is the zero module!
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Meeting ID: 821 5368 6539
Passcode: 098489