On a theorem of Fuller

[摘要] Let e and f be primitive idempotents in a semiperfect ring R with radical J. Suppose that (i) fR/fJ congruent to Soc(eR(R)), which is essential in eR(R); and (ii) Re/Je congruent to Soc((R)Rf), which is essential in (R)Rf. We prove that the following are equivalent: (1) both (eRe)eR and Rf(fRf) are linearly compact; (2) both eR(R) and (R)Rf are injective; (3) eR(R) is injective and Rf(fRf) is linearly compact; and (4) (eRe)eR is linearly compact and (R)Rf is injective. This generalizes an old theorem of Fuller and a recent theorem of Baba and Oshiro. (C) 1997 Elsevier Science B.V.

[发布日期] 1997-10-24