关于半模复形同调理论的若干研究

Some Studies of Homology Theory on Semimodule Complex

在半模范畴中,针对半环和半模的加法都无逆运算,利用泛代数的思想,在同余的观点下定义了半模复形和复形链映射及复形同调函子,给出了一个半模复形为正合列的条件,并把环模上的连接同态定理在一定的条件下推广到了半模上,且得到了较弱的半模复形的长正合列定理.

In the category of semimodules,the concept of semimodule complex and chain mapping and complex homology functor are defined in view of congruence using the idea of universal algebra,for the addition of the semiring and semimodule are no inverse operation,also a condition of complex to be exact sequences is given. The connecting homomorphism theorem is extended to the semimodules under certain conditions,and got the weakly long exact sequence theorem of semimodules complex.