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The Hochschild cohomology ring modulo nilpotence of a stacked monomial algebra

Edward L. Green, Nicole Snashall (2006)

Colloquium Mathematicae

This paper studies the Hochschild cohomology of finite-dimensional monomial algebras. If Λ = K/I with I an admissible monomial ideal, then we give sufficient conditions for the existence of an embedding of K [ x , . . . , x r ] / x a x b f o r a b into the Hochschild cohomology ring HH*(Λ). We also introduce stacked algebras, a new class of monomial algebras which includes Koszul and D-Koszul monomial algebras. If Λ is a stacked algebra, we prove that H H * ( Λ ) / K [ x , . . . , x r ] / x a x b f o r a b , where is the ideal in HH*(Λ) generated by the homogeneous nilpotent elements. In...

The importance of rational extensions

Frans Loonstra (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The rational completion M ¯ of an R -module M can be characterized as a τ M -injective hull of M with respect to a (hereditary) torsion functor τ M depending on M . Properties of a torsion functor depending on an R -module M are studied.

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