Answer to Question #22730 in Abstract Algebra for Irvin

Question #22730

Let R be a commutative Q-algebra generated by x1, x2, . . . with the relations xixj = 0 for all i, j. Show that R is semiprimary (that is, rad R is nilpotent, and R/rad R is semisimple), but neither artinian nor noetherian.

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