| Divisible modules and localization |
| Lidia Angeleri Hügel |
| 关键词： |
| 主要内容：A Matlis domain is a commutative domain R whose ring of quotients Q has projective dimension one. The properties of these domains have been extensively studied in the literature.In [18], Kaplansky proved that the quotient field of a local domain has projective dimension one if and only if it is countably generated. Hamsher, in his beautiful paper [16],showed that if R is a Matlis domain any countably generated submodule of Q/R can be embedded in a countably generated direct summand of Q/R. This result generalizes Kaplansky’s theorem because if R is local then Q/R is indecomposable. Hamsher’s results were completed by Lee in [21] proving that Q has projective dimension at most one if and only if Q/R decomposes into a direct sum of countably generated modules... |
| 《2005 Elsevier》 |
| 全文下载请进入http://hightech.stlib.cn/tpi_1/sysasp/include/index.asp |
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