Y.X.

### Questions (259)

 6 Is that true that each non-initial object has elements under this definition of ETCS? 6 $X(C) = \{\text{nilpotent elements in$C$}\}$ is not a scheme 6 Reference of the connection of category theory and logic(foundation of mathematics) 6 Being a PID is not a local property 6 Prove that if a commutative ring $R$ is integral domain, then the polynomial ring $R[x]$ is also an integral domain.

### Reputation (3,617)

 +10 (From Axler)Why does the basis satisfy the required conditions? +10 How to formally prove that a degree 2 or 3 polynomial f(x) ∈ F[x] is irreducible if and only if it has no root in F +10 Prove that in a field $F$ of characteristic $p$, $f(x)=x^p −x−a$ is either irreducible or splits over +10 Is that true that each non-initial object has elements under this definition of ETCS?

 1 Is $Spec(\Bbb R[x,y]/\langle xy\rangle)[ \frac{1}{ x−y} ]$ connected? 0 How can we conclude $n\xi_j^{n-1}=\prod_{i \ne j}(\xi_{i}-\xi_{j})$ from $x^n-1=\prod_{i}(x-\xi_{i})$

### Tags (180)

 1 algebraic-geometry × 23 0 field-theory × 47 1 affine-schemes × 11 0 abstract-algebra × 45 1 idempotents × 3 0 extension-field × 32 1 connectedness × 2 0 polynomials × 29 0 real-analysis × 52 0 logic × 28

### Bookmarks (332)

 425 Proofs that every mathematician should know. [closed] 246 “Which answer in this list is the correct answer to this question?” 206 Good books and lecture notes about category theory. 147 Overview of basic results about images and preimages 120 What are good books to learn graph theory?