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 clas...

We give a criterion for the existence of a super-decomposable pure-injective module over an arbitrary serial ring.

The model theory of abelian groups was developed by Szmielew ([28] quantifier elimination and decidability) and Eklof & Fisher [4], who observed that K1saturated abelian groups are pure injective. Eklof & Fisher related the structure theory of pure injective abelian groups with their model theory. The extension of this theory to modules over arbitrary rings became possible after the work of Bau...

Abstract Assume that k is an algebraically closed field and A a finite-dimensional wild -algebra. Recently, L. Gregory M. Prest proved in this case the width of lattice all pointed -modules undefined. Hence result Ziegler implies there exists super-decomposable pure-injective -module, if base countable. Here we give different straightforward proof fact. Namely, show special family -modules, cal...