Extensions of injectivity and coherent rings

摘要

For a ring D and a subring C , let R[D,C] = {(d(1),...,d(n),c,c,...): d(i) is an element of D, c is an element of C, n >= 1}, a subring of Pi(i=1)(infinity), and let D proportional to D = {((a)(b)(0)(a)) : a, b is an element of D}, a subring of IM2 (D). In this article, various conditions are obtained for R[D,C] and D proportional to D to be right (m,n)-injective (in particular, P-injective, f-injective, FP-injective), right coherent, and right FC. Right nonsingular right (m,n)-injective rings are characterized using their maximal right quotient rings.