query: The only idempotent element in $\Bbb Z_{51}$ are $0$ and $1$.
positive_passages.docid: 102112
positive_passages.text: Idempotents in $\mathbb Z_n$
negative_passages.docid: 36631
negative_passages.text: Is $[0,1] \cap \Bbb Q$ a compact subset of $\Bbb Q$?
negative_passages.docid: 103518
negative_passages.text: If $J$ is the ideal generated by all idempotents in a prime ideal, then $R/J$ has only trivial idempotents
negative_passages.docid: 87238
negative_passages.text: $(1 2)(3 4)$ does not commute with any nonidentity element of odd order in $A_5$.
negative_passages.docid: 110545
negative_passages.text: Space $X$ such that $H_i(X,\mathbb{Z})\neq 0$ but $H_i(X,\mathbb{Z}_3)= 0$
negative_passages.docid: 30753
negative_passages.text: Showing there is no ring whose additive group is isomorphic to $\mathbb{Q}/\mathbb{Z}$
negative_passages.docid: 121643
negative_passages.text: Why isn't the zero ring the field with one element?
negative_passages.docid: 16971
negative_passages.text: Prove that no ordinal is an element of itself
negative_passages.docid: 148343
negative_passages.text: The sum of the elements in a field of at least three elements is 0
negative_passages.docid: 77735
negative_passages.text: When $\Bbb Z_n$ is a domain. Counterexample to $ab \equiv 0 \Rightarrow a\equiv 0$ or $b\equiv 0\pmod n$
negative_passages.docid: 42528
negative_passages.text: Prove that every idempotent element is not nilpotent element.
negative_passages.docid: 19740
negative_passages.text: What's are all the prime elements in Gaussian integers $\mathbb{Z}[i]$
negative_passages.docid: 102250
negative_passages.text: Subset of $C[0,1]$ is nowhere dense
negative_passages.docid: 44100
negative_passages.text: Prove that identity element is unique
negative_passages.docid: 89535
negative_passages.text: fake proof of $\forall a. \forall b. a = b \to 1 = 0$
negative_passages.docid: 50133
negative_passages.text: The sum of odd powered real numbers equals zero implies the numbers are inverses
negative_passages.docid: 5022
negative_passages.text: Can a set containing $0$ be purely imaginary?