Acyclicity of Tate constructions

We prove that a Tate construction A <u(1), ..., u(n) / partial derivative ( u(i)) = z(i)> over a differential graded algebra A, on cycles z(1),...z(n), in A(greater than or equal to1), is acyclic if and only if the map of grad ed-commutative algebras H-0(A)[y(1),...,y(n)] --> H(A), with y(i) --> cls(z (i)), is an isomorphism. This is used to establish that if a large homomorp hism R --> S has an acyclic closure R <U > with sup{i / U-i not equal 0} = s < infinity, then s is either 1 or an even integer. (C) 2001 Elsevier Scie nce B.V. All rights reserved.