满足(accr)环的I-adic完备化及其平坦性

The I adic Completion and Its Flatness for Rings Satisfying (accr)

中文关键词:  满足（accr）的环  反向极限  I－adic完备化

英文关键词:rings satisfying （accr）  inverse limit  I-adic completion.

中文摘要:

      满足（ａｃｃｒ）环是比Ｎｏｅｔｈｅｒ环更广泛的一类环，本文讨论了满足（ａｃｃｒ）环的Ｉ－ａｄｉｃ完备化及其平坦性问题，把Ｎｏｅｔｈｅｒ环的有关结果推广到满足（ａｃｃｒ）环上，同时也改进了［１］中的结果．

英文摘要:

      The class of rings satisfying (accr) is larger than that of Noetherian rings. The I-adic completion and its flatness for rings satisfying (accr) are discussed. Some important properties of Noetherian rings can be generalized to rings of this class; the results in have been improved.