… subring of S such that S is the maximal right quotient ring, and also a left quotient ring, of
R. Then there is a "matrix subsystem" {Dij} contained in K and a ring isomorphism R→ Res S …

… It is a sequel to an earlier work, and we refer to it for the double annihilator condition for
injective and quasi-injective modules and the development of the maximal quotient ring; see Ref. …

… If R is a right Goldie, semiprime ring, and K is a right ideal of R and if k*eK* then thinking of
k* as a mapping of A' in Q, the right quotient ring, since QR is injective there is a qeQ so that k*…

… rings, and if A is a quotient ring of Band B is a quotient ring is a maximal quotient ring of A is
a quotient ring … is a quotient ring of B, then A is a quotient ring of R by (1). But B is a maximal …

… (An injective module MR is said to be Σ-injective iff the direct sum of arbitrarily many copies
… where R denotes the Johnson's maximal quotient ring of Ry is the injective hull of RR, we …

… of a module is always injective if and only if the ring is left-… any ring R a module E is an
indecomposable, injective module if … is a left-Noetherian ring, then every injective Jϋ-module has a …

… quotient ring of R. Thus, for noncommutative R, in general £QM = does not imply that M is a
dense right Rsub module… ingular that £QM = implies that M is dense, since then Q is injective. …

… are injective: simple modules, quasi-injective modules, or proper cyclic … is injective as an
(2?//)-module. Inasmuch as R/I is a semiprime right Goldie ring with classical right quotient ring ζ…

… injective [3] as a right R-module, hence the injective hull of R [2]. A ring R has a semisimple
maximal right quotient ring … is finite, where a right R-module M is of finite dimension if every …

… Thus we conclude that (Rx'^y^O and hence Q is a left quotient ring of R. Conversely assume
that Q is a left quotient ring. Let N be a finitely … Next we shall prove the "if" p injective, every …