(a) Assume that M is a torsion module
. Then Ex[t.sup.1.sub.A]([T.sub.2], M) = 0 in the long exact sequence because [T.sub.2] is in add T and M is torsion.
We may define a specialization of [T.sub.M] by specializing [X.sup.R] to (x - 1), [Y.sup.R] to (y - 1), and [(XY).sup.N] to the cardinality of N for each torsion module
Conway (George Washington U.) applies the Euler characteristic to map coloring, proves the spectral theorem for hermitian and normal linear transformations on a finite-dimensional Hilbert space, and develops the structure of a finitely generated torsion module
. Exercises follow each section.