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Answer to Question #22759 in Abstract Algebra for sanches

Question #22759
Let R be a commutative domain that is not a field. Show that not always R is not J-semisimple implies R is semilocal, if R is a noetherian domain.
Expert's answer
For instance, the 2-dimensionalnoetherian domain R = Z[[x]] is not J-semisimple by factthat J(R)=J(Z)+xZ[[x]] = xZ[[x]] – nonzero, but has infinitely many maximal
ideals: (p, x) for p = 2, 3, 5, . . . .

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