强n-凝聚环  

Strongly n-Coherent Rings

作　　者：朱占敏[1] 

机构地区：[1]嘉兴学院数学系,浙江嘉兴314001

出　　处：《数学年刊（A辑）》2017年第3期313-326,共14页Chinese Annals of Mathematics

摘　　要：设R是一个环,n是一个正整数.右R-模M称为强n-内射的,如果从任一自由右R-模F的任一n-生成子模到M的同态都可扩张为F到M的同态;右R-模V称为强n-平坦的,如果对于任一自由右R-模F的任一n-生成子模T,自然映射VT→VF是单的;环R称为左强n-凝聚的,如果自由左R-模的n-生成子模是有限表现的;环R称为左n-半遗传的,如果R的每个n-生成左理想是投射的.本文研究了强n-内射模,强n-平坦摸及左强n-凝聚环.通过模的强n-内射性和强n-平坦性概念,作者还给出了强n-凝聚环和n-半遗传环的一些刻画.Let R be a ring and n a fixed positive integer. A right R-module M is called strongly n-injective if every R-homomorphism from an n-generated submodule of a free right R-module F to M extends to a homomorphism of F to M; a right R-module V is said to be strongly n-flat, if for every n-generated submodule T of a free right R-module F, the canonical map V T→V F is monic; a ring R is called left strongly n-coherent if every n-generated submodule of a free left R-module is finitely presented; ring R is said to be left n-semihereditary if every n-generated left ideal of R is projective. The author studies strongly n-injective modules, strongly n-flat modules and left strongly n-coherent rings. Using the concepts of strongly n-injectivity and strongly n-flatness of modules, the author also presents some characterizations of strongly n-coherent rings and n-semihereditary rings.

关 键 词：强n-内射模 强n-平坦模 强n-凝聚环 m半遗传环 

分 类 号：O153.3[理学—数学]