【摘要】 用环R上的矩阵研究了R 模的一些同调性质.对于任给的基数α,β以及β×α行有限矩阵A,证明了Ext1R(R(α) /R(β)A,M)=0当且仅当Mα/rMα(R(β)A) HomR(R(β)A,M)当且仅当rMβlR(β) (A)=AMα,进一步推广了(m,n) 内射性的概念,并从矩阵的零化子,同态的分解和同调群等角度给出(α,β) 平坦性的等价刻画,从而使(m,n) 平坦模,f 投射模和n 投射模统一到(α,β) 平坦模的概念之下.此外还给出了左R ML模的一个刻画和R(β)A是左R ML模的等价条件,从而把凝聚环、(m,n) 凝聚环、π凝聚环等概念统一到(α,β) 凝聚环的概念之下.更多还原

【Abstract】 Some homological properties of R-modules were investigated by matrices over a ring R.Given two cardinal numbers α,β and an α×β row-finite matrix A,it was proved that Ext 1_R (R (α) /R (β) A,M)=0 if and only if M_α/r_ M_α (R (β) A) Hom_R(R (β) A,M) if and only if r_ M_β l_ R (β) (A)=AM_α.Thus,the notion of (m,n)-injectivity was extended.Moreover,(α,β)-flatness was characterized via annihilators of matrices,factorizations of homomorphisms as well as homological groups so that (m,n)-flat modules,f-projective modules and n-projective modules were consolidated under the notion of (α,β)-flat modules.Furthermore,a characterization of left R-ML modules and some equivalent conditions for R (β) A to be left R-ML were presented.Consequently,the notions of coherent rings,(m,n)-coherent rings and π-coherent rings were consolidated under that of (α,β)-coherent rings.更多还原