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Construction and decoding of BCH codes over chain of commutative rings
(2012)
In this paper, we present a new construction and decoding of BCH codes over certain rings. Thus, for a nonnegative integer t, let A0 ⊂ A1 ⊂···⊂ At−1 ⊂ At be a chain of unitary commutative rings, where each Ai is constructed ...
Locally nilpotent groups of units in tiled rings
(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2010)
We consider locally nilpotent subgroups of units in basic tiled rings A, over local rings O which satisfy a weak commutativity condition. Tiled rings are generalizations of both tiled orders and incidence rings. If, in ...
BASS CYCLIC UNITS AS FACTORS IN A FREE GROUP IN INTEGRAL GROUP RING UNITS
(WORLD SCIENTIFIC PUBL CO PTE LTD, 2011)
Marciniak and Sehgal showed that if u is a non-trivial bicyclic unit of an integral group ring then there is a bicyclic unit v such that u and v generate a non-abelian free group. A similar result does not hold for Bass ...
Maximal cyclic subgroups of the groups of units of Galois rings: a computational approach
(Springer, 2017-09-01)
We present a computational approach based on algorithmic techniques to obtain maximal cyclic subgroups of the groups of units in Galois rings. The objective of this work was to provide an automated methodology to obtain ...
ALTERNATING UNITS AS FREE FACTORS IN THE GROUP OF UNITS OF INTEGRAL GROUP RINGS
(CAMBRIDGE UNIV PRESS, 2011)
Let G be a group of odd order that contains a non-central element x whose order is either a prime p >= 5 or 3(l), with l >= 2. Then, in U(ZG), the group of units of ZG, we can find an alternating unit u based on x, and ...
INVOLUTIONS AND FREE PAIRS OF BASS CYCLIC UNITS IN INTEGRAL GROUP RINGS
(WORLD SCIENTIFIC PUBL CO PTE LTD, 2011)
Let ZG be the integral group ring of the finite nonabelian group G over the ring of integers Z, and let * be an involution of ZG that extends one of G. If x and y are elements of G, we investigate when pairs of the form ...
CENTRAL UNITS IN METACYCLIC INTEGRAL GROUP RINGS
(TAYLOR & FRANCIS INC, 2008)
In this article, we give a method to compute the rank of the subgroup of central units of ZG, for a finite metacyclic group, G, by means of Q-classes and R-classes. Then we construct a multiplicatively independent set u ...
A note on units of finite local rings in an ascending chain
(2012)
In this paper we present matrices over unitary finite commutative local rings connected through an ascending chain of containments, whose elements are units of the corresponding rings in the chain such that the McCoy ranks ...
Integral group ring of the Suzuki sporadic simple group
(KOSSUTH LAJOS TUDOMANYEGYETEM, 2008)
Using the Luthar-Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the Suzuki sporadic simple group Suz. As a consequence, for this group we confirm ...