2
votes
0answers
83 views

On one class of Euclidean lattices

Let $\Lambda\subset \mathbb Z^3$ be 3D lattice with a basis $$a_1=\left(\begin{smallmatrix} a_{11} \\ a_{21}\\ a_{31} \end{smallmatrix}\right),a_2=\left(\begin{smallmatrix} a_{12} \\ a_{22}\\ a_{32} ...
3
votes
0answers
222 views

PAC field : Algebraically closed field :: ? : Henselian local ring

I'm wondering if the following exists in the world as a definition. I'll use the word "pseudo-Henselian." I'll restrict to DVRs for simplicity. I'd want to call a DVR $(R,\mathfrak{m})$ ...
1
vote
1answer
312 views

equivalence of definitions of Carmichael numbers

I would like to prove the equivalence of the two most common definitions of a composite integer $n > 1$ being a Carmichael number: $a^n \equiv a \mod n $ for all $a$ $\iff a^{n-1} \equiv 1 \mod n$ ...
2
votes
2answers
585 views

On figurate numbers

Do you know a text where I can find a definition of polygonal number that is both geometrically and operationally sound? I've basically seen two ways in which this topic is approached in the ...
5
votes
2answers
604 views

Unitary groups over number fields

When defining unitary groups over number fields, one usually takes $F$ to be a totally real number field, $E$ a CM quadratic extension of $F$, and $V$ a hermitian space attached to $E/F$. Then $U(V)$ ...