关于有限平坦表现模  

On Finitely Flatly Presented Modules

作　　者：谢燕萍[1] 尹芳芳[1] 李德梅[1] 周德旭[1] 

机构地区：[1]福建师范大学数学与计算机科学学院,福建福州350007

出　　处：《莆田学院学报》2013年第5期18-21,共4页Journal of putian University

基　　金：福建省自然科学基金资助项目(2009J01003);福建师范大学本科教学改革研究资助项目(I201302015)

摘　　要：将有限表现模限制在平坦维数≤1,得到有限平坦表现模及其性质,利用有限平坦表现模类给出了其Ext-正交模即FFP-内射模,刻画了右F-凝聚环与右F-正则环。在环的几乎优越扩张S≥R下,证明了S为右F-凝聚环当且仅当R为右F-凝聚环,S为右F-正则环当且仅当R为右F-正则环。Finitely presented modules was restricted to modules with flat dimension ≤ 1 to obtain finitely flatly presented modules and their properties. The Ext-orthogonal module of finitely flatly presented modules, namely FFP-injective module was given to characterize right F-coherent rings and right F-regular rings. Under an almost excellent extension S≥R of rings, it was proven that S is a right F-coherent ring if and only if R is a right F-coherent ring, S is a right F-regular ring if and only if R is a tight F- regular ring.

关 键 词：有限平坦表现模 FFP 内射模 右F-凝聚环 右F-正则环 

分 类 号：O153.3[理学—数学]