Study of excellent rings and its neighborhood

(1)在[K]中，我给出了Notherian环有算术Cohen-Macaulaytion的一个充要条件，通过引入p-标准序列的新概念，改进了它的构造。计算了正则模的局部上同调模。(3)1978年，Falings证明了零化子定理。1982年，他猜想零化子定理在较弱的假设下成立。我肯定地回答了他的猜想。(4)1991年，Hukene[H]证明了一致Artin-Rees定理和一致Briancon-Skoda定理。他还推测，这些定理在较弱的假设下成立。关于这些定理，我给出了肯定的回答[H，猜想2.13]。[F1]G.Faltings，ueber Annulatoren lokaler Kohomologiegruppen，Arch.Math。[F2]G.Faltings，Der EndlichkeitsSatz in der lokalen Kohomologie，Math.Ann.255(1981)，45--56.[H]C.Huneke，Notherian环上的一致界，Invent.Math.107(1992)，203-223.[K]T.Kawasaki，表亲上同调的有限性.

(1) In [K], I gave a necessarily and sufficient condition for a Noetherian ring to have an arithmetic Cohen-Macaulayfication.I refine its construction by introducing a new notion, called p-standard sequences.(2) In [K], computed the depth of the canonical module. I compute local cohomology modules of the canonical module.(3) In 1978, Faltings prove the annihilator theorem. In 1982, he conjectured that the annihilator theorem holds under weaker assumption. I give an affirmative answer to his conjecture.(4) In 1991, Hukene [H] proved the uniform Artin-Rees theorem and the uniform Briancon-Skoda theorem. He also conjectured that these theorem hold under weaker assumption. I give an affirmative answer to [H, Conjecture 2.13] concerning these theorems.[F1] G.Faltings, Ueber die Annulatoren lokaler Kohomologiegruppen, Arch.Math. (Basel) 30 (1978), 473--476.[F2] G.Faltings, Der Endlichkeitssatz in der lokalen Kohomologie, Math.Ann.255 (1981), 45--56.[H] C.Huneke, Uniform bounds in noetherian rings, Invent.Math. 107 (1992), 203--223.[K] T.Kawasaki, Finiteness of Cousin cohomologies.