On Some Algebras of Infinite Cohomological Dimension

If A is a nilpotent algebra of finite rank over afield K, the cohomological dimension of A is greater than or equal to 3.We prove here that the dimension is actually infinite. As a consequence, we deduce that the cohomological dimension of the Grassmann ring on n-letters over a commutative semi-simple ring is infinite. This provides, incidentally, counter-examples to certain questions in Homological Algebra.