Hochschild cohomology rings of algebras \(k[X]/(f)\)
Let \(k\) be a commutative ring, \(f\in k[X]\) a monic polynomial. The author investigates the structure of the Hochschild cohomology ring for the \(k\)-algebra \(k[X]/(f)=A_f\). The subring of classes of even degree depends very precisely on the ring structure of \(A_f\). For the full cohomology ring particularly the situation is studied, where \(f\) is a power of an irreducible separable polynomial or \(f=X^n\). The latter case contains modular group algebras of cyclic \(p\)-groups and, therefore, generalises earlier results [\textit{Th. Holm}, Commun. Algebra 24, No. 6, 1957-1969 (1996; Zbl 0853.16016)].
scientific article; zbMATH DE number 1428680