The projectivity of Ext(T,A) as a module over E(T) - MSP

386 JOSEPH N. FADYN
/ = {1, 2, 3, •}. Since T P
(A) is reduced and unbounded, for each
ίel, we may choose v t
e T P
(A) with the property that (v %
) is a cyclic
summand of T P
(A) and such that O(ι> t
) < O(v i+1
), i = 1, 2, 3, . Say
(v,) = Z(p w 0 for i = 1, 2, 3, . Now, let fc< e Horn (A, ^(p 00 )) be
defined by:
hJVi) = ——, Λ< = 0 otherwise .
Let:
f(^) - α M
+ a Hi
+ + a bjH
.
where a bj{
eE(A) hji
for all j = 1, 2, , &,. Define β^E{A) by:
Then the computation:
/5.(x;.) = 0, & = 1 otherwise .
0 - α/r(0) = ψ(h t
β t
) - α &l
.A + a bu
β t
+ • + α 6fc