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Pure injective envelopes of finite length modules over a Generalised Weyl Algebra
"... We investigate certain pure-injective modules over generalised Weyl algebras. We consider pure-injective hulls of finite length modules, the elementary duals of these, torsionfree pure-injective modules and the closure in the Ziegler spectrum of the category of finite length modules supported on a n ..."
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We investigate certain pure-injective modules over generalised Weyl algebras. We consider pure-injective hulls of finite length modules, the elementary duals of these, torsionfree pure-injective modules and the closure in the Ziegler spectrum of the category of finite length modules supported on a nondegenerate orbit of a generalized Weyl algebra. We also show that this category is a direct sum of uniserial categories and admits almost split sequences. We find parallels to but also marked contrasts with the behaviour of pure injective modules over finite-dimensional algebras and hereditary orders.
The Torsionfree Part Of The Ziegler Spectrum Of RG When R Is A Dedekind Domain And G Is A Finite Group
"... Introduction For every ring S with identity, the (right) Ziegler spectrum of S, Zg S , is the set of (isomorphism classes of) indecomposable pure injective (right) S-modules. The Ziegler topology equips Zg S with the structure of a topological space. A typical basic open set in this topology is of t ..."
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Introduction For every ring S with identity, the (right) Ziegler spectrum of S, Zg S , is the set of (isomorphism classes of) indecomposable pure injective (right) S-modules. The Ziegler topology equips Zg S with the structure of a topological space. A typical basic open set in this topology is of the form ('= ) = fM 2 Zg S : j '(M) : '(M) \ (M) j > 1g where ' and are pp-formulas (with at most one free variable) in the rst order language L S for S-modules; let ['= ] denote the closed set Zg S ('= ). There is an alternative way
