On the derived length of units in group algebra
Let be a finite group , a field of characteristic and let be the group of units in . We show that if the derived length of does not exceed , then must be abelian.
On the Group of Norm 1 Elements in a Division Algebra.
On the isomorphism problem for modular group algebras of elementary abelian-by-cyclic p-groups
Let G be a finite p-group and let F be the field of p elements. It is shown that if G is elementary abelian-by-cyclic then the isomorphism type of G is determined by FG.
On the Jacobson radical and unit groups of group álgebras.
In this paper, we study the situation as to when the unit group U(KG) of a group algebra KG equals K*G(1 + J(KG)), where K is a field of characteristic p > 0 and G is a finite group.
On the multiplicative subgroup of a group ring
On the unit group of a semisimple group algebra
We give the characterization of the unit group of , where is a finite field with elements for prime and denotes the special linear group of matrices having determinant over the cyclic group .
On unit group of finite semisimple group algebras of non-metabelian groups up to order 72
We characterize the unit group of semisimple group algebras of some non-metabelian groups, where is a field with elements for prime and a positive integer . In particular, we consider all 6 non-metabelian groups of order 48, the only non-metabelian group of order 54, and 7 non-metabelian groups of order 72. This completes the study of unit groups of semisimple group algebras for groups upto order 72.
-clean rings.
Partial isometries and EP elements in rings with involution.
Produit tensoriel de matrices, homologie cyclique, homologie des algèbres de Lie
On munit, naturellement, d’un surproduit l’algèbre extérieure de l’homologie cyclique d’une -algèbre commutative ( étant un corps de caractéristique zéro) à l’aide du produit de Loday-Quillen. On munit d’un surproduit l’homologie de l’algèbre de Lie du groupe linéaire général de à l’aide du produit tensoriel de matrices. On montre que l’isomorphisme d’algèbres de Hopf de Loday-Quillen est compatible avec les surproduits définis ci-dessus. On obtient ainsi une interprétation du produit de Loday-Quillen,...
Puissances divisées des algèbres simpliciales en caractéristiques deux et séries de Poincaré de certains anneaux locaux.
Remarks on the structure of the multiplicative monoid of integers modulo m.
Ring elements as sums of units
In an Artinian ring R every element of R can be expressed as the sum of two units if and only if R/J(R) does not contain a summand isomorphic to the field with two elements. This result is used to describe those finite rings R for which Γ(R) contains a Hamiltonian cycle where Γ(R) is the (simple) graph defined on the elements of R with an edge between vertices r and s if and only if r - s is invertible. It is also shown that for an Artinian ring R the number of connected components of the graph...
Rings with many idempotents.
Structure of the Unit Group of FD10
2000 Mathematics Subject Classification: 16U60, 20C05.The structure of the unit group of the group algebra FD10 of the dihedral group D10 of order 10 over a finite field F has been obtained.Supported by National Board of Higher Mathematics, DAE, India.
Subgroups of finite index in an additive group of a ring.
Subgroups of the basic subgroup in a modular group ring
Sylow P-Subgroups of Abelian Group Rings
2000 Mathematics Subject Classification: Primary 20C07, 20K10, 20K20, 20K21; Secondary 16U60, 16S34.Let PG be the abelian modular group ring of the abelian group G over the abelian ring P with 1 and prime char P = p. In the present article,the p-primary components Up(PG) and S(PG) of the groups of units U(PG) and V(PG) are classified for some major classes of abelian groups. Suppose K is a first kind field with respect to p in char K ≠ p and A is an abelian p-group. In the present work, the p-primary...
Symmetric units and group identities in group algebras. I.
The isomorphic description of torsion units in commutative group rings over fields with positive characteristic.