Resumen de Height preserving linear transformations on semisimple K-algebras

Valerio Talamanca

• Let $A$ be a semisimple, commutative, finite $K$-algebra, $K$ a number field. In this paper we study a family of height functions on $A$ with special regard toward the characterization of height preserving $K$-linear transformations. The height functions that we examine are defined as a product over $\mathcal{M}_K$ (the set of places of $K$) of $v$-adic norms on the various completions $A_v = A\otimes_KK_v$.