location:  Publications → journals
Search results

Search: MSC category 12F ( Field extensions )

 Expand all        Collapse all Results 1 - 6 of 6

1. CMB 2014 (vol 57 pp. 538)

Ide, Joshua; Jones, Lenny
 Infinite Families of $A_4$-Sextic Polynomials In this article we develop a test to determine whether a sextic polynomial that is irreducible over $\mathbb{Q}$ has Galois group isomorphic to the alternating group $A_4$. This test does not involve the computation of resolvents, and we use this test to construct several infinite families of such polynomials. Keywords:Galois group, sextic polynomial, inverse Galois theory, irreducible polynomialCategories:12F10, 12F12, 11R32, 11R09

2. CMB 2014 (vol 57 pp. 735)

Cagliero, Leandro; Szechtman, Fernando
 On the Theorem of the Primitive Element with Applications to the Representation Theory of Associative and Lie Algebras We describe of all finite dimensional uniserial representations of a commutative associative (resp. abelian Lie) algebra over a perfect (resp. sufficiently large perfect) field. In the Lie case the size of the field depends on the answer to following question, considered and solved in this paper. Let $K/F$ be a finite separable field extension and let $x,y\in K$. When is $F[x,y]=F[\alpha x+\beta y]$ for some non-zero elements $\alpha,\beta\in F$? Keywords:uniserial module, Lie algebra, associative algebra, primitive elementCategories:17B10, 13C05, 12F10, 12E20

3. CMB 2006 (vol 49 pp. 11)

Bevelacqua, Anthony J.; Motley, Mark J.
 Going-Down Results for $C_{i}$-Fields We search for theorems that, given a $C_i$-field $K$ and a subfield $k$ of $K$, allow us to conclude that $k$ is a $C_j$-field for some $j$. We give appropriate theorems in the case $K=k(t)$ and $K = k\llp t\rrp$. We then consider the more difficult case where $K/k$ is an algebraic extension. Here we are able to prove some results, and make conjectures. We also point out the connection between these questions and Lang's conjecture on nonreal function fields over a real closed field. Keywords:$C_i$-fields, Lang's ConjectureCategories:12F, 14G

4. CMB 2006 (vol 49 pp. 113)

Ledet, Arne
 $\PSL(2,2^n)$-Extensions Over $\mathbb F_{2^n}$ We construct a one-parameter generic polynomial for $\PSL(2,2^n)$ over $\mathbb F_{2^n}$. Categories:12F12, 12E10

5. CMB 2002 (vol 45 pp. 422)

Ledet, Arne
 On the Essential Dimension of Some Semi-Direct Products We give an upper bound on the essential dimension of the group $\mathbb{Z}/q\rtimes(\mathbb{Z}/q)^*$ over the rational numbers, when $q$ is a prime power. Category:12F10

6. CMB 2001 (vol 44 pp. 313)

 Images of mod $p$ Galois Representations Associated to Elliptic Curves We give an explicit recipe for the determination of the images associated to the Galois action on $p$-torsion points of elliptic curves. We present a table listing the image for all the elliptic curves defined over $\QQ$ without complex multiplication with conductor less than 200 and for each prime number~$p$. Keywords:Galois groups, elliptic curves, Galois representation, isogenyCategories:11R32, 11G05, 12F10, 14K02