完全有素的乘法模和网

Complete Non-primeless Multiplicative Modules and Reticulations

若 R是带单位元的交换环 ,M是完全有素的乘法模 ,则 :(1 )映射 φ:P PM是从Spec(R)到 Spec(M)的双射 ;(2 ) Zariski拓扑空间 (Spec(R) ,T)和 Stone拓扑空间 (Spec(R*M) ,T*M)同胚 ;(3 ) (R*M,λ)构成 R的一个网。

It is shown that if R is a commutative ring with 1 and M is a complete non primeless multiplicative module, then (1)the mapping φ:PPM of spec(R) onto spec(M) is a bijection; (2) the toplogical spaces (Spec(R),T) and (Spec(R  M), T  M) are homeomorphic; (3)(R  M, λ) is a reticulation for a commutative ring R.