2007/10/19 by Chen, Sheng
#13C10 #15A23 #15A54 #37B10 #Dynamical Systems (math.DS) #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.0710.3746
The paper studies algebraic strong shift equivalence of matrices over n-variable polynomial rings over a principal ideal domain D(n≤ 2). It is proved that in the case n=1, every non-zero matrix over D[x] has a full rank factorization and every non-nilpotent matrix over D[x] is algebraically strong shift equivalent to a nonsingular matrix. In the case n=2, an example of non-nilpotent matrix over ℝ[x,y,z]=ℝ[x][y,z], which can not be algebraically shift equivalent to a nonsingular matrix, is given.