Hochschild homology ($H{H}_n(R,M)$)

Hochschild homology is an important concept in algebraic topology and homological algebra, often used to study algebraic structures, particularly associative algebras. It was introduced by Gerhard Hochschild in the 1940s. ### Definition and Construction Hochschild homology is typically defined for a unital associative algebra \( A \) over a field \( k \) (or more generally, over a commutative ring).