Jansian环上的余遗传挠对

Cohereditary Torsion Pair over Jansian Ring

给出了jansian环的定义,等价刻画了jansian环上的余遗传挠对,证明了R-模范畴上所有余遗传挠对构成的集合R-Ctors在R是jansian环时是一个格,且在jansian环尺上,R-Ctors与R-Jan之间存在格反同构,引进了使M为挠模的最小余遗传挠对ξ(M)=∧{σ=(T,F)|σ是余遗传挠对,并且M∈T},并给出ξ(M)一些格上的性质．

We introduce the definition of jiansian ring. The eohereditary torsion pair over jansian ring is characterized;We show that the set R-Ctors which is constructed by all of the eohereditary torsion pairs over R-Ctors is a lattice. There exists lattice inverse isomorphism between R-Ctors and R-Jan. We introduce the smallest cohereditary torsion pair ξ^-（M）=∧{σ=（T,F）｜σ is cohereditary torsion pair, M∈ T）,such that M is torsion module. Some lattice＇s properties of ξ^-（M） is given.