query: $I^2=I$ but $I$ not a direct summand
positive_passages.docid: 151794
positive_passages.text: Can an ideal in a commutative integral domain be its own square?
negative_passages.docid: 94383
negative_passages.text: Prove that $A^TD-C^TB=I$
negative_passages.docid: 120092
negative_passages.text: Express the complex numbers given in Problem in the form $a+ib$
negative_passages.docid: 150310
negative_passages.text: A finite sum of reciprocals of complex numbers cannot be confined to a half-plane
negative_passages.docid: 77764
negative_passages.text: Is "$a + 0i$" in every way equal to just "$a$"?
negative_passages.docid: 84213
negative_passages.text: How to show $n\sum_{i=1}^n {x_i^2} \ge (\sum_{i=1}^n{x_i})^2$
negative_passages.docid: 31116
negative_passages.text: Matrix given by $a_{ij} = 1/(i+j)$ is non-singular.
negative_passages.docid: 98808
negative_passages.text: Finite Sum $\sum_{i=1}^n\frac i {2^i}$
negative_passages.docid: 47313
negative_passages.text: What is $i^i$ and $(i^i)^i$
negative_passages.docid: 101320
negative_passages.text: How to tell $i$ from $-i$?
negative_passages.docid: 79425
negative_passages.text: Prove the direct product of nonzero complex numbers under multiplication.
negative_passages.docid: 128566
negative_passages.text: Proving $2$ generates $(\mathbb{Z}/19\mathbb{Z})^*$ by only looking at a few powers
negative_passages.docid: 117533
negative_passages.text: $|A-\lambda I|$ and $|\lambda I-A|$
negative_passages.docid: 127047
negative_passages.text: How to show that $\sum_{i=1}^n | \langle f, f_i\rangle |^2 \leq \Vert f \Vert^2$
negative_passages.docid: 77486
negative_passages.text: What is the value of $i^i$?
negative_passages.docid: 85626
negative_passages.text: prove $\sum_{i=1}^{n}(x_i-\bar{x})^2\lt\sum_{i=1}^{n}(x_i-a)^2$
negative_passages.docid: 153532
negative_passages.text: Proving $a^2$ is even $\implies$ $a$ is even by contradiction