相对无挠模

Relative torsionless modules

讨论了相对于忠实平衡双模ω的相对无挠模的一些性质,给出了一个左或右Noether环是QF-环的一些等价条件,并证明了当ω为广义倾斜双模时,ω-无挠模与ω-1-合冲模以及ω-1-挠自由模均是等价的。研究了相对无挠模类的扩张封闭性。部分结果推广了关于经典的无挠模的结论。

Some elementary properties of relative torsionless modules with respect to a faithful and balanced bimodule are studied. Some equivalent conditions for a left or right Noether ring is a QF-ring is gotten. It is proved that a finitely generated module is an ω-torsionless module if and only if it is an ω-l-syzygy module if and only if it is an ω-l-torsion- free module when ω is a generalized tilting bimodule. Moreover, the extension closure of the class of ω-torsionless modules is investigated, and some classical results are generalized to the relative case.