Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 41, No. 1, pp. 291-301 (2000)

Hochschild Cohomology Rings of Algebras $k[X]/(f)$

Thorsten Holm

Institut für Algebra und Geometrie, Otto-von-Guericke-Universität Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany e-mail:

Abstract: Let $k$ be a commutative ring with unity and let $f\in k[X]$ a monic polynomial. We determine the ring structure of the Hochschild cohomology for the $k$-algebra $k[X]/(f)$. This generalizes results of [A] on the Hochschild cohomology rings of modular group algebras of cyclic groups over fields. \item{[A]} Cibils, C.; Solotar, A.: Hochschild cohomology algebra and Hopf bimodules of an abelian group. Arch. Math. 68 (1997), 17-21.

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