Maranda’s theorem for pure-injective modules and duality

Abstract Let R be a discrete valuation domain with field of fractions Q and maximal ideal generated by $\pi $ . $\Lambda an -order such that $Q\Lambda is separable -algebra. Maranda showed there exists $k\in \mathbb {N}$ for all -lattices L M , if $L/L\pi ^k\simeq M/M\pi ^k$ then $L\simeq M$ Moreover, complete indecomposable -lattice, also indecomposable. We extend Maranda’s theorem to the class -reduced -torsion-free pure-injective -modules. As application this extension, we show order over Dedekind separable, lattice open subsets part right Ziegler spectrum isomorphic left Furthermore, k as in theorem, $H(M)$ hull $H(M)/H(M)\pi $M/M\pi use result give characterization -modules describe hulls certain