Torsion-free module

In algebra, a torsion-free module is a module over a ring such that 0 is the only element annihilated by a regular element (non zero-divisor) of the ring.

In integral domains the regular elements of the ring are its nonzero elements, so in this case a torsion-free module is one such that 0 is the only element annihilated by some non-zero element of the ring. Some authors work only over integral domains and use this condition as the definition of a torsion-free module, but this does not work well over more general rings, for if the ring contains zero divisors then the only module satisfying this condition is the zero module.

单词	Torsionfree module
释义	Torsionfree module 英语百科 Torsion-free module In algebra, a torsion-free module is a module over a ring such that 0 is the only element annihilated by a regular element (non zero-divisor) of the ring. In integral domains the regular elements of the ring are its nonzero elements, so in this case a torsion-free module is one such that 0 is the only element annihilated by some non-zero element of the ring. Some authors work only over integral domains and use this condition as the definition of a torsion-free module, but this does not work well over more general rings, for if the ring contains zero divisors then the only module satisfying this condition is the zero module.
随便看	Rhynchanthus beesianus Rhynchelytrum Rhynchelytrum repens Rhynchites auratus Rhynchites bicolor Rhynchites giganteus rhynchitid rhynchitids rhynchium atrum rhynchium quinquecinctum brunneum rhyncho rhynchobatids Rhynchobatini Rhynchobatus djiddensis Rhynchobdellae Rhynchobdellida Rhynchocela rhynchoceph Rhynchocephalia rhynchocephalian rhynchocephalias rhynchocephalic rhynchociline rhynchocinetes rugulosus rhynchocinetids

Torsionfree module

Torsion-free module