幺半群上的广义内射S-系

摘要

In this paper the properties of quasi-injective S-acts, pseudo-injective S-acts, ker-injective S-acts and C-injective S-acts, especially the properties of the linear equation sys- tems on these kinds of generalized injective S-acts, are discussed. For example, A is a ker- injective S-act if and only if every A-compatible linear equation system on the S-act B, an arbitrary kernel of A, is soluble in B. A is a C-injective S-acts if and only if every A-compatible linear equation system on the S-act B which is isomorphic to some component of A, is soluble in B. What is more, we discuss the properties of amalgam coproduct of pseudo-injective S-acts, ker-injective S-acts and C-injective S-acts. Finally, we give a sufficient condition under which an S-acts is ker-injective if and only if it is C-injective S-acts.%本文考虑拟内射、伪内射、核内射以及支内射S-系的性质，重点讨论这些广义内射S-系的上的线性方程组的性质．例如，A是核内射D系当且仅当A的任意收缩核B上的任意A-相容线性方程组在口上是可解的；A是支内射S-系当且仅当同构于A的任一分支的S-系B上的任意A-相容线性方程组在B上是可解的．进而讨论了伪内射、核内射以及支内射S-系的融合余积的性质．最后给出了一个充分条件，基于此条件核内射和支内射S-系是等价的．