GreginGre

 14 axioms of real numbers without multiplication 10 If $R$ is a noetherian ring, then $ab=1$ implies $ba=1$ $\forall a,b\in R$ 8 Submodules of finitely generated modules 7 How does the quotient ring $\Bbb Z[x]/(x^2-x,4x+2)$ look like? 7 The monster continued fraction

### Reputation (9,771)

 +15 How to define a bijection between a set of maps from a Cartesian product to an abelian group to a set of bilinear maps to that same group? +45 A basis of eigenvectors for Galois extension +100 If $R$ is a noetherian ring, then $ab=1$ implies $ba=1$ $\forall a,b\in R$ +15 Determine the Galois group of the splitting field of $f(x) = x^4+x+t \in F_2(t)[x]$

### Questions (18)

 7 Which groups can be proven to be simple using Iwasawa criterion? 4 Polynomials for which the induced polynomial map is zero 4 Nice (and rather short) applications of module theory for a book chapter 3 $G$ $p$-group, $G^{ab}\simeq \mathbb{Z}/p\mathbb{Z}$ implies $G\simeq \mathbb{Z}/p\mathbb{Z}$ 2 Is $\mathbb{Z}/n\mathbb{Z}[X]/(f)$ a principal ideal ring?

### Tags (234)

 327 abstract-algebra × 176 59 galois-theory × 28 105 group-theory × 56 49 algebraic-number-theory × 22 104 ring-theory × 55 46 modules × 21 81 linear-algebra × 62 43 number-theory × 33 81 field-theory × 36 38 matrices × 34

### Bookmarks (251)

 83 Alice and Bob play the determinant game 69 Are there any valid continuous Sudoku grids? 43 Can a number be equal to the sum of the squares of its prime divisors? 26 How to prove this inequality $x^2_{n}\le\frac{8}{3}$ 22 The “co-small” topology on the naturals?