query: Is there an integral domain $R$ with ideal $I$ such that $I^2 = I$ and $I$ is nontrivial?
positive_passages.docid: 151794
positive_passages.text: Can an ideal in a commutative integral domain be its own square?
negative_passages.docid: 551
negative_passages.text: Why is a finite integral domain always field?
negative_passages.docid: 128550
negative_passages.text: Algebraic field extension and intermediate integral domain
negative_passages.docid: 135152
negative_passages.text: Non-UFD integral domain such that prime is equivalent to irreducible?
negative_passages.docid: 512
negative_passages.text: Finding generator for the ideal generated by $a$ and $b$ in an euclidean domain
negative_passages.docid: 13174
negative_passages.text: Show that $A[X]/(aX+b)$ is an integral domain
negative_passages.docid: 74370
negative_passages.text: $P$ is a prime ideal of $R$ iff $R/P$ is an integral domain. : $P≠R$
negative_passages.docid: 132289
negative_passages.text: Associates in Integral Domain
negative_passages.docid: 14158
negative_passages.text: Prove that $R$ is an integral domain $\Leftrightarrow$ $R[x]$ is an integral domain
negative_passages.docid: 90314
negative_passages.text: Maximal ideals in $R[x]$
negative_passages.docid: 90599
negative_passages.text: Trouble with proving $A$ is an integrally closed domain $\Rightarrow$ $A[t]$ is integrally closed domain
negative_passages.docid: 116453
negative_passages.text: Is any quotient of a Euclidean domain by a prime ideal a Euclidean domain?
negative_passages.docid: 15137
negative_passages.text: Does $IJ=IK\implies J=K$ always hold for integral domain and finitely generated nonzero ideal $I$?
negative_passages.docid: 16984
negative_passages.text: Finite extension of domains : preimage of non-zero ideal is non-zero?
negative_passages.docid: 108896
negative_passages.text: Prime ideal in a polynomial ring over an integrally closed domain
negative_passages.docid: 112560
negative_passages.text: Simple Noetherian domain which is not a division ring
negative_passages.docid: 24351
negative_passages.text: The ring $\Bbb Z\left [\frac{-1+\sqrt{-19}}{2}\right ]$ is not a Euclidean domain