Let I be a left ideal of Rand let(I: R) = {r RI rR I}.

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Let I be a left ideal of Rand let(I: R) = {r ϵ RI rR ⊂ I}.

(a) (I: R) is an 1deal of R. If I is regular, then (I: R) is the largest ideal of R that is contained in I.

(b) If I is a regular maximal left ideal of R and A ≅ R/ I, then α(A) = (I : R). Therefore J(R) = ∩ (I : R), where I runs over all the regular maximal left ideals of R.

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