Seminar • Symbolic Computation | Computer Algebra • Annihilators of Square Matrices Over Rings with Zero Divisors

Please note: This seminar will take place in DC 1302.

Roswitha Rissner, Department of Mathematics
Alpen-Adria-Universität Klagenfurt, Austria

Given a square matrix B' over a (commutative) ring S, the null ideal N_0(B') is the ideal consisting of all polynomials f in S[X] for which f(B')=0. In the case that S=R/J is the residue class ring of a ring R modulo an ideal J, we can equivalently study the so-called J-ideals

N_J(B) =  { f in  R[X]  |  f(B) in M_n(J) }

where B is a preimage of B' under the projection modulo J. If R is a principal ideal domain it suffices to determine a finite number of polynomials in order to describe all J-ideals of B. In this talk we discuss algorithmic approaches to compute these polynomials.

References

• Null ideals of matrices over residue class rings of principal ideal domains: http://dx.doi.org/10.1016/j.laa.2016.01.004
• Computing J-ideals of a matrix over a principal ideal domain: http://dx.doi.org/10.1016/j.laa.2017.03.028