2017/11/24 by Salce, Luigi, Virili, Simone
#13C60 #13F30 #16S50 #37A35 #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1711.09080
We extend the notion of intrinsic entropy for endomorphisms of Abelian groups to endomorphisms of modules over an Archimedean non-discrete valuation domain R, using the natural non-discrete length function introduced by Northcott and Reufel for such a category of modules. We prove that this notion of entropy is a length function for the category of R[X]-modules, it satisfies (a suitably adapted version of) the Intrinsic Algebraic Yuzvinski Formula and that it is essentially the unique invariant for Mod(R[X]) with these properties.