Almost finitely-presented modules. (Chinese. English summary) Zbl 1274.16008
Summary: This paper characterizes coherent rings and semi-hereditary rings by using almost finitely-presented modules. By studying relations between almost finitely-presented modules and generalized finitely-presented modules, some equivalent conditions about almost finitely-presented modules and coherent rings and semi-hereditary rings are obtained. Previous conclusions are improved, and the modules used to characterize coherent rings are reduced to almost finitely-presented modules.
MSC:
16D80 | Other classes of modules and ideals in associative algebras |
16E60 | Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc. |
16P70 | Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras) |