scholarly journals Zero divisors of support size 3 in group algebras and trinomials divided by irreducible polynomials over GF(2)

Author(s):  
Alireza Abdollahi ◽  
Zahra Taheri
Filomat ◽  
2017 ◽  
Vol 31 (10) ◽  
pp. 2917-2923
Author(s):  
Mehmet Koroglu ◽  
Irfan Siap

Constacyclic codes are preferred in engineering applications due to their efficient encoding process via shift registers. The class of constacyclic codes contains cyclic and negacyclic codes. The relation and presentation of cyclic codes as group algebras has been considered. Here for the first time, we establish a relation between constacyclic codes and group algebras and study their algebraic structures. Further, we give a method for constructing constacyclic codes by using zero-divisors in group algebras. Some good parameters for constacyclic codes which are derived from the proposed construction are also listed.


1976 ◽  
Vol 15 (3) ◽  
pp. 453-454 ◽  
Author(s):  
D. Handelman ◽  
J. Lawrence

We prove that most group algebras of free products have left zero divisors that are not right zero divisors.


1997 ◽  
Vol 56 (2) ◽  
pp. 209-215
Author(s):  
Ramesh V. Garimella

For a locally compact Abelian group G and a commutative Banach algebra B, let L1(G, B) be the Banach algebra of all Bochner integrable functions. We show that if G is compact and B is a nonunital Banach algebra without nontrivial zero divisors, then (i) all derivations on L1(G, B) are continuous if and only if all derivations on B are continuous, and (ii) each epimorphism from a Banach algebra X onto L1(G, B) is continuous provided every epimorphism from X onto B is continuous. If G is noncompact then every derivation on L1(G, B) and every epimorphism from a commutative Banach algebra onto L1(G, B) are continuous. Our results extend the results of Neumann and Velasco for nonunital Banach algebras.


1998 ◽  
Vol 07 (06) ◽  
pp. 837-841 ◽  
Author(s):  
DALE ROLFSEN ◽  
JUN ZHU

We begin with the observation that the group algebras [Formula: see text] of Artin's braid groups have no zero divisors or nontrivial units. This follows from the recent discovery of Dehornoy that braids can be totally ordered by a relation < which is invariant under left multiplication. We then show that there is no ordering of Bn, n ≥ 3 which is simultaneously left and right invariant. Nevertheless, we argue that the subgroup of pure braids does possess a total ordering which is invariant on both sides. This follows from a general theorem regarding orderability of certain residually nilpotent groups. As an application, we show that the pure braid groups have no generalized torsion elements, although full braid groups do have such elements.


1988 ◽  
Vol 51 (6) ◽  
pp. 496-499 ◽  
Author(s):  
Andreas Neumann
Keyword(s):  

2000 ◽  
Vol 227 (1) ◽  
pp. 362-364 ◽  
Author(s):  
Ian J. Leary
Keyword(s):  

2021 ◽  
pp. 1-6
Author(s):  
Jitender Singh ◽  
Sanjeev Kumar

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