Trivial units in commutative group algebras.
Two examples of inverse semigroups algebras.
Über den Träger von Blöcken
Über Ringe die von ihren Einheitengruppen erzeugt werden
Une propriété des anneaux d'entiers.
Uniform Distribution Classified.
Unique Factorization In Group-Rings
Unique factorization in group-rings.
Unit groups of group algebras of some small groups
Let be a group algebra of a group over a field and the unit group of . It is a classical question to determine the structure of the unit group of the group algebra of a finite group over a finite field. In this article, the structure of the unit group of the group algebra of the non-abelian group with order over any finite field of characteristic is established. We also characterize the structure of the unit group of over any finite field of characteristic and the structure of...
Unitary subgroup of integral group rings.
Let A be a finite abelian group and G = A x 〈b〉, b2 = 1, ab = a-1, ∀a ∈ A. We find generators up to finite index of the unitary subgroup of ZG. In fact, the generators are the bicyclic units. For an arbitrary group G, let B2(ZG) denote the group generated by the bicyclic units. We classify groups G such that B2(ZG) is unitary.
Unitary subgroup of integral groups rings.
Unitary units in modular group algebras.
Units in group rings of crystallographic groups
In [3], the authors initiated a technique of using affine representations to study the groups of units of integral group rings of crystallographic groups. In this paper, we use this approach for some special classes of crystallographic groups. For a first class of groups we obtain a normal complement for the group inside the group of normalized units. For a second class of groups we show that the Zassenhaus conjectures ZC1 and ZC3 are valid. This generalizes the results known for the infinite dihedral...
Units of F5kD10
2000 Mathematics Subject Classification: 20C05, 16U60, 16S84, 15A33.The Structure of the Unit Group of the Group Algebra of the group D10 over any field of characteristic 5 is established in terms of split extensions of cyclic groups.
Valuations and group algebras
Valuations and Semi-Valuations of Graded Domains.
Vector invariant ideals of abelian group algebras under the actions of the unitary groups and orthogonal groups
Let be a finite field of characteristic and a field which contains a primitive th root of unity and . Suppose that a classical group acts on the -vector space . Then it can induce the actions on the vector space and on the group algebra , respectively. In this paper we determine the structure of -invariant ideals of the group algebra , and establish the relationship between the invariant ideals of and the vector invariant ideals of , if is a unitary group or orthogonal group....
Warfield Invariants in Abelian Group Algebras
Warfield invariants in abelian group rings.
Let R be a perfect commutative unital ring without zero divisors of char(R) = p and let G be a multiplicative abelian group. Then the Warfield p-invariants of the normed unit group V (RG) are computed only in terms of R and G. These cardinal-to-ordinal functions, combined with the Ulm-Kaplansky p-invariants, completely determine the structure of V (RG) whenever G is a Warfield p-mixed group.
Weak Baer modules over graded rings
In [2], Fuchs and Viljoen introduced and classified the -modules for a valuation ring R: an R-module M is a -module if for each divisible module X and each torsion module X with bounded order. The concept of a -module was extended to the setting of a torsion theory over an associative ring in [14]. In the present paper, we use categorical methods to investigate the -modules for a group graded ring. Our most complete result (Theorem 4.10) characterizes -modules for a strongly graded ring R...