半对偶模的环扩张及相关模

Ring extensions with respect to semidualizing modules and related modules

设R是交换环,利用同调代数的方法,研究半对偶模K的环扩张R∝K及其上的投射模、平坦模、有限表示模等.证明了对于任意(R∝K)-模M和平坦R-模Q以及任意整数k≥1,都有同构Ext^(t)_(R∝K)(M,(R∝K)■RQ)■Ext^(t)_(R∝K)(M,■RQ).当Q是平坦R-模时,(R∝K)-模(R∝K)■RQ的内射维数小于等于R-模K■RQ的内射维数.

Let R be a commutative ring,using methods of homological of algebra,the ring extension(R∝K) with respect to the semidualizing module K and projective modules,flat modules,finitely persented modules et al over it are investigated.It is proved that there is the isomorphism Ext^(t)_(R∝K)(M,(R∝K)■RQ)■Ext^(t)_(R∝K)(M,■RQ)for any(R∝K)-module M and flat R-moodule Q and any integer k≥1.When 0 is a flat R-module,the injective dimension of(R∝K)module(R∝K)■RQis less than or equal to the injective dimension of R-module K■RQ.