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

Zero divisors and units with small supports in group algebras of torsion-free groups

Communications in Algebra ◽

10.1080/00927872.2017.1344688 ◽

2017 ◽

Vol 46 (2) ◽

pp. 887-925 ◽

Cited By ~ 1

Author(s):

Alireza Abdollahi ◽

Zahra Taheri

Keyword(s):

Free Groups ◽

Group Algebras ◽

Zero Divisors ◽

Torsion Free

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A class of constacyclic codes from group algebras

Filomat ◽

10.2298/fil1710917k ◽

2017 ◽

Vol 31 (10) ◽

pp. 2917-2923

Author(s):

Mehmet Koroglu ◽

Irfan Siap

Keyword(s):

Cyclic Codes ◽

Group Algebras ◽

Constacyclic Codes ◽

Algebraic Structures ◽

Engineering Applications ◽

Negacyclic Codes ◽

Zero Divisors ◽

First Time

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.

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Left and right zero divisors in group algebras

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700022887 ◽

1976 ◽

Vol 15 (3) ◽

pp. 453-454 ◽

Cited By ~ 2

Author(s):

D. Handelman ◽

J. Lawrence

Keyword(s):

Group Algebras ◽

Left Zero ◽

Free Products ◽

Zero Divisors ◽

Left And Right

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

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On continuity of derivations and epimorphisms on some vector-valued group algebras

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700030938 ◽

1997 ◽

Vol 56 (2) ◽

pp. 209-215

Author(s):

Ramesh V. Garimella

Keyword(s):

Banach Algebra ◽

Banach Algebras ◽

Commutative Banach Algebra ◽

Group Algebras ◽

Locally Compact Abelian Group ◽

Locally Compact ◽

Zero Divisors ◽

Integrable Functions ◽

Vector Valued ◽

Nontrivial Zero

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.

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BRAIDS, ORDERINGS AND ZERO DIVISORS

Journal of Knot Theory and Its Ramifications ◽

10.1142/s0218216598000425 ◽

1998 ◽

Vol 07 (06) ◽

pp. 837-841 ◽

Cited By ~ 17

Author(s):

DALE ROLFSEN ◽

JUN ZHU

Keyword(s):

General Theorem ◽

Nilpotent Groups ◽

Braid Groups ◽

Group Algebras ◽

Left Multiplication ◽

Zero Divisors ◽

Left And Right

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.

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