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Constant-plus-ideal non-Noetherian subring

The subring

R = K + X Y K [X, Y]

is not Noetherian. Its ideals

(X Y)_{R} ⊊ (X Y, X Y^{2})_{R} ⊊ \dots

form a strict ascending chain because multiplying by a nonconstant element of

R

introduces at least a second power of

X

.

 Ancestors (5)

 Incoming links (1)

Solution