广义逆多项式模的子模和投射覆盖

Submodules and Projective Covers of Modules of Generalized Inverse Polynomials

从子模、本质子模、多余子模等方面探讨广义逆多项式模M[S]与其系数模M之间的关系.定义左R 模同态λ∶M→N的诱导左[[RS,≤]] 模同态λ ∶M[S]→N[S],得到结论:若(M[S],λ )是N[S]的投射覆盖,则(M,λ)是N的投射覆盖.

Consider the modules of generalized inverse polynomials M[S]over the rings of generalized power series[[R^(S,≤)]],and discuss the relations between M[S]and M on submodules,essential submodules and superfluous submodules.Introduce the homomorphism λ~*:M[S]→N[S] induced by λ∶M→N,and show that:If(M[S],λ~*)is a projective cover of N[S],then(M,λ)is a projective cover of N.