环的左自由正规化扩张和拟Excellent扩张

Left Free Normalizing Extensions and Quasi-ExcellentExtensions of Rings

本文引进了环的左自由正规化扩张和拟Ｅｘｃｅｌｅｎｔ扩张，并将环的Ｅｘｃｅｌｅｎｔ扩张的一些性质推广到了左自由正规化扩张和拟Ｅｘｃｅｌｅｎｔ扩张，主要讨论了几乎Ｎｏｅｔｈｅｒ性，正则性，凝聚性和半遗传性．

The left free normalizing extension andquasi-excellent extension of a ring are introduced. Some properties ofexcellent extension of a ring are generalized to left free normalizingextension and quasi-excellent extension. The main results are about thealmost Noetherian property, regularity, coherent property andsemiheredity.