Geodesic
Maximal Quotient Rings of Endomorphism Rings of E(RR)-Torsionfree Generators
Canadian journal of mathematics, Tome 33 (1981) no. 3, pp. 585-605

Voir la notice de l'article provenant de la source Cambridge University Press

Let R be a ring with identity and let H = End (E(RR)) and Q = Dou(E(R R )) = End(H E(R R )). Then Lambek [11] showed that Q is always isomorphic to Qm(R), the maximal right quotient ring of R. And Johnson [10] and Wong-Johnson [26] proved that Qm(R) is regular and right self-injective if and only if R is right non-singular, and then H is isomorphic to Qm(R), too. Moreover, Sandomierski [18] showed that Qm(R) is semi-simple Artinian if and only if R is right finite dimensional and right non-singular. And it is well known that Qm(R) is a quasi-Frobenius ring if and only if E(RR) is a rational extension of RR and the ACC holds on right annihilators of subsets of E(RR).The purpose of this paper is to give some module-theoretic generalizations of these results. Let PR be an E(PR)-torsionless generator, and let S = End(PR ), H = End(E(PR)) and Q = Dou(E(PR)). 
Izawa, Tatsuo. Maximal Quotient Rings of Endomorphism Rings of E(RR)-Torsionfree Generators. Canadian journal of mathematics, Tome 33 (1981) no. 3, pp. 585-605. doi: 10.4153/CJM-1981-048-3
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