可消半模的正合列

Exact Sequence of Cancellable Semimodules

设A和B是S-半模,f:A→B是半模同态.ΔA和Kf分别定义为ΔA={(a,b)∈A×A|a+m=b+m,存在m∈A}和Kf={(a,b)∈A×A|f(a)+m=f(b)+m,存在m∈B}.将Kf和ΔA同时缩小为所规定的Kerf和ΔA,重新给出了monic和epic不同的定义,从不同的角度对某类特殊的半模—可消半模的正合列进行了刻画.

Let A, B be S-semimodule,f：A→ B be homomorphism of semimodule. ˉ△A and Kf are defined as ˉ△A = {（ a, b）∈ A × A │ a ＋ m = b＋ m,some m ∈ A and Kf = │（a,b） ∈ A ×A │f（a） ＋ m =f（b） ＋ m,some m ∈ B }. Through deflating Kf and ˉ△A synchronously into Kerf and ,54 , reconstructing the definition of monic and epic, the description theorems of exact sequence of cancellable senfimodule, are given from other point of view.