Computation Of The Homological Invariant Tor_m～(?)(Z,Z) Of Non-unital Ring A

As a branch of algebra ,homological algebra is not only a the-ory,but also a useful tool for researching ring. In this paper ,the author, using the resolution theory of projective modules, studies the important excision problem in algebraic K-theory by calculating the homological invariant Tor_m^A (Z, Z).ln chapter one, he gives a brief introduction to homological algebra , algebraic K-theory and the background of this paper .Let A be a non-unital ring,A = A Z.In chapter two, the author gives a free resolution of A -module Z ,where A = sZ_st .According to the free resolution ,he obtains the valuation of Tor_m^A(Z, Z)(m ≥ 1) . In chapter three, a free resolution of A -module Z is given when he considers (s,t₁) = (s, t₂) =.... (s,t_r) and A = s(Z_st₁ Z_st2 .... Z_str). From the free resolution ,he gets the valuation of Tor_m^A(Z, Z)(m > 1).