2018/10/06 by Abdulaziz Deajim, Deajim, A., Lhoussain El Fadil +1
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Coding theory and cryptography #Advanced Differential Equations and Dynamical Systems
paper · pdf · doi:10.48550/arxiv.1810.02987
Let R be a Dedekind ring, K its quotient field, and L=K(\α) a\nfinite field extension of K defined by a monic irreducible polynomial\nf(x)\∈ R[x]. We give an easy version of Dedekind's criterion which\ncomputationally improves those versions know in the literature. We further use\nthis result to give a sufficient condition for the integral closedness of\nR[\α] when f(x)=xn-a. In case R is a ring of integers of a number\nfield, we give yet sufficient and necessary conditions for this to hold,\ngeneralizing and improving in both cases some known results in this direction.\nSome highlighting examples are also given.\n