The largest strong left quotient ring of a ring
نویسنده
چکیده
For an arbitrary ring R, the largest strong left quotient ring Ql (R) of R and the strong left localization radical lR are introduced and their properties are studied in detail. In particular, it is proved that Ql (Q s l (R)) ≃ Q s l (R), l s R/ls R = 0 and a criterion is given for the ring Ql (R) to be a semisimple ring. There is a canonical homomorphism from the classical left quotient ring Ql,cl(R) to Q s l (R) which is not an isomorphism, in general. The objects Q s l (R) and l s R are explicitly described for several large classes of rings (semiprime left Goldie ring, left Artinian rings, rings with left Artinian left quotient ring, etc).
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