软正合序列的若干性质

Properties of Soft Exact Sequences

利用模论和软模的基本性质讨论软同态的分解性质.首先,定义单的软模同态和软模序列的正合;其次,证明软同态都可以分解为一个满的软同态和一个单的软同态的复合;最后讨论软正合序列的基本性质,给出几类简单的软模序列正合的等价条件,并利用两个软正合序列构造一个新的软正合序列.

By using module theory and the basic properties of soft modules,we discussed the decomposition properties of soft homomorphism.Firstly,we defined a single soft homomorphism of soft modules and soft exact sequence.Secondly,we proved that every soft homomorphism could be decomposed into the composition of an epimorphism and a monomorphism.Finally,we discussed the basic properties of soft exact sequences,and gave equivalent conditions for several kinds of simple soft modulus sequence to be exact,and constructed a new soft exact sequence by using two soft exact sequences.