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Anneaux d’entiers stablement libres sur [ H 8 × C 2 ]

Jean Cougnard (1998)

Journal de théorie des nombres de Bordeaux

Le groupe H 8 × C 2 est le plus petit groupe pour lequel existent des modules stablement libres non libres. On montre que toutes les classes d’isomorphisme de tels modules peuvent être représentées une infinité de fois par des anneaux d’entiers. On applique un travail de classification de Swan, pour cela on doit construire explicitement des bases normales d’entiers d’extensions à groupe H 8 ; cela se fait en liant un critère de Martinet avec une construction de Witt.

Annihilator ideals of finite dimensional simple modules of two-parameter quantized enveloping algebra U r , s ( 𝔰𝔩 2 )

Yu Wang, Xiaoming Li (2023)

Czechoslovak Mathematical Journal

Let U be the two-parameter quantized enveloping algebra U r , s ( 𝔰𝔩 2 ) and F ( U ) the locally finite subalgebra of U under the adjoint action. The aim of this paper is to determine some ring-theoretical properties of F ( U ) in the case when r s - 1 is not a root of unity. Then we describe the annihilator ideals of finite dimensional simple modules of U by generators.

Another 80-dimensional extremal lattice

Mark Watkins (2012)

Journal de Théorie des Nombres de Bordeaux

We show that the unimodular lattice associated to the rank 20 quaternionic matrix group SL 2 ( F 41 ) S ˜ 3 GL 80 ( Z ) is a fourth example of an 80-dimensional extremal lattice. Our method is to use the positivity of the Θ -series in conjunction with an enumeration of all the norm 10 vectors. The use of Aschbacher’s theorem on subgroups of finite classical groups (reliant on the classification of finite simple groups) provides one proof that this lattice is distinct from the previous three, while computing the inner product...

Antiassociative groupoids

Milton Braitt, David Hobby, Donald Silberger (2017)

Mathematica Bohemica

Given a groupoid G , , and k 3 , we say that G is antiassociative if an only if for all x 1 , x 2 , x 3 G , ( x 1 x 2 ) x 3 and x 1 ( x 2 x 3 ) are never equal. Generalizing this, G , is k -antiassociative if and only if for all x 1 , x 2 , ... , x k G , any two distinct expressions made by putting parentheses in x 1 x 2 x 3 x k are never equal. We prove that for every k 3 , there exist finite groupoids that are k -antiassociative. We then generalize this, investigating when other pairs of groupoid terms can be made never equal.

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