Functors on Finite Vector Spaces and Units in Abelian Group Rings

1986 ◽  
Vol 29 (1) ◽  
pp. 79-83 ◽  
Author(s):  
Klaus Hoechsmann
Keyword(s):  
Abelian Group ◽  
Group Ring ◽  
Elementary Abelian Group ◽  
Vector Spaces ◽  
Group Rings ◽  
Cyclic Subgroups ◽  
Group Of Units ◽  
Finite Vector ◽  
Finite Vector Spaces

AbstractIf A is an elementary abelian group, let (A) denote the group of units, modulo torsion, of the group ring Z[A]. We study (A) by means of the compositewhere C and B run over all cyclic subgroups and factor-groups, respectively. This map, γ, is known to be injective; its index, too, is known. In this paper, we determine the rank of γ tensored (over Z);with various fields. Our main result depends only on the functoriality of

Units in Integral Group Rings for Order pq

1995 ◽  
Vol 47 (1) ◽  
pp. 113-131
Author(s):  
Klaus Hoechsmann
Keyword(s):  
Abelian Group ◽  
Group Ring ◽  
Finite Index ◽  
Finite Abelian Group ◽  
Integral Group Ring ◽  
Group Rings ◽  
Integral Group ◽  
Integral Group Rings ◽  
Group Of Units ◽  
Cyclotomic Units

AbstractFor any finite abelian group A, let Ω(A) denote the group of units in the integral group ring which are mapped to cyclotomic units by every character of A. It always contains a subgroup Y(A), of finite index, for which a basis can be systematically exhibited. For A of order pq, where p and q are odd primes, we derive estimates for the index [Ω(A) : Y(A)]. In particular, we obtain conditions for its triviality.

scholarly journals On λ-fold partitions of finite vector spaces and duality

2011 ◽  
Vol 311 (4) ◽  
pp. 307-318 ◽  
Author(s):  
S. El-Zanati ◽  
G. Seelinger ◽  
P. Sissokho ◽  
L. Spence ◽  
C. Vanden Eynden
Keyword(s):  
Vector Spaces ◽  
Finite Vector ◽  
Finite Vector Spaces

scholarly journals Bijective methods in the theory of finite vector spaces

1984 ◽  
Vol 37 (1) ◽  
pp. 80-84 ◽  
Author(s):  
Albert Nijenhuis ◽  
Anita E Solow ◽  
Herbert S Wilf
Keyword(s):  
Vector Spaces ◽  
Finite Vector ◽  
Finite Vector Spaces

scholarly journals The number of idempotents in abelian group rings

Filomat ◽  
2012 ◽  
Vol 26 (4) ◽  
pp. 719-723
Author(s):  
Peter Danchev
Keyword(s):  
Abelian Group ◽  
Group Ring ◽  
Group Rings ◽  
Arbitrary Characteristic

Suppose that R is a commutative unitary ring of arbitrary characteristic and G is a multiplicative abelian group. Our main theorem completely determines the cardinality of the set id(RG), consisting of all idempotent elements in the group ring RG. It is explicitly calculated only in terms associated with R, G and their divisions. This result strengthens previous estimates obtained in the literature recently.

Outer Partial Actions and Partial Skew Group Rings

2015 ◽  
Vol 67 (5) ◽  
pp. 1144-1160 ◽  
Author(s):  
Patrik Nystedt ◽  
Johan Öinert
Keyword(s):  
Abelian Group ◽  
Dynamical Systems ◽  
Group Ring ◽  
Group Rings ◽  
Partial Action ◽  
Unital Ring ◽  
Different Types ◽  
Outer Action ◽  
Skew Group Rings ◽  
Skew Group Ring

AbstractWe extend the classical notion of an outer action α of a group G on a unital ring A to the case when α is a partial action on ideals, all of which have local units. We show that if α is an outer partial action of an abelian group G, then its associated partial skew group ring A *α G is simple if and only if A is G-simple. This result is applied to partial skew group rings associated with two different types of partial dynamical systems.

Units in Group Rings of the Infinite Dihedral Group

1991 ◽  
Vol 34 (1) ◽  
pp. 83-89 ◽  
Author(s):  
Maciej Mirowicz
Keyword(s):  
Group Ring ◽  
Integral Domain ◽  
Dihedral Group ◽  
Group Rings ◽  
Finitely Generated ◽  
Group Of Units ◽  
Group D

AbstractThis paper studies the group of units U(RD∞) of the group ring of the infinite dihedral group D∞ over a commutative integral domain R. The structures of U(Z2D∞) and U(Z3D∞) are determined, and it is shown that U(ZD∞) is not finitely generated.

scholarly journals Integral Group Rings with Nilpotent Unit Groups

1976 ◽  
Vol 28 (5) ◽  
pp. 954-960 ◽  
Author(s):  
César Polcino Milies
Keyword(s):  
Finite Group ◽  
Group Ring ◽  
Unit Element ◽  
Group Rings ◽  
Integral Group ◽  
Integral Group Rings ◽  
Group Of Units ◽  
The Subject ◽  
A Finite Group

Let R be a ring with unit element and G a finite group. We denote by RG the group ring of the group G over R and by U(RG) the group of units of this group ring.The study of the nilpotency of U(RG) has been the subject of several papers.

scholarly journals Kinematic formulas for finite vector spaces

1998 ◽  
Vol 179 (1-3) ◽  
pp. 121-132 ◽  
Author(s):  
Daniel A. Klain
Keyword(s):  
Vector Spaces ◽  
Finite Vector ◽  
Finite Vector Spaces
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