On modules with trivial self-extensions

Graded self-injective algebras “are” trivial extensions

Article history: Received 20 March 2009 Available online 9 June 2009 Communicated by Michel Van den Bergh Dedicated to Professor Helmut Lenzing on the occasion of his seventieth birthday

The $w$-FF property in trivial extensions

‎Let $D$ be an integral domain with quotient field $K$‎, ‎$E$ be a $K$-vector space‎, ‎$R = D propto E$ be the trivial extension of $D$ by $E$‎, ‎and $w$ be the so-called $w$-operation‎. ‎In this paper‎, ‎we show that‎ ‎$R$ is a $w$-FF ring if and only if $D$ is a $w$-FF domain; and‎ ‎in this case‎, ‎each $w$-flat $w$-ideal of $R$ is $w$-invertible.

Self-extensions of Verma Modules and Differential Forms on Opers

We compute the algebras of self-extensions of the vacuum module and the Verma modules over an affine Kac-Moody algebra ĝ in suitable categories of Harish-Chandra modules. We show that at the critical level these algebras are isomorphic to the algebras of differential forms on various spaces of opers associated to the Langlands dual Lie algebra of g, whereas away from the critical level they bec...

אn-Free Modules With Trivial Duals

In the first part of this paper we introduce a simplified version of a new Black Box from Shelah [11] which can be used to construct complicated אn-free abelian groups for any natural number n ∈ N. In the second part we apply this prediction principle to derive for many commutative rings R the existence of אn-free R-modules M with trivial dual M ∗ = 0, where M∗ = Hom(M, R). The minimal size of ...

Extensions of Baer and quasi-Baer modules