Central Zero Divisors in Group Algebras

On the Zero Divisors of Hopf Algebras

In an attempt to study the zero divisors in infinite Hopf algebras, we study two non-trivial examples of non-group ring infinite Hopf algebras and show that a variant of Kaplansky’s classical zero divisor conjecture holds for these two Hopf algebras.

Smarandache-Zero Divisors in Group Rings

The study of zero-divisors in group rings had become interesting problem since 1940 with the famous zero-divisor conjecture proposed by G.Higman [2]. Since then several researchers [1, 2, 3] have given partial solutions to this conjecture. Till date the problem remains unsolved. Now we introduce the notions of Smarandache zero divisors (S-zero divisors) and Smarandache week zero divisors (S-wea...

Constructing zero divisors in the higher dimensional Cayley-Dickson algebras

In this paper we give methods to construct zero divisors in the Cayley–Dickson algebras An=R 2 for n larger than 4. Also we relate the set of zero divisors with suitable Stiefel manifolds.

Codes from zero-divisors and units in group rings

We describe and present a new construction method for codes using encodings from group rings. They consist primarily of two types: zero-divisor and unit-derived codes. Previous codes from group rings focused on ideals; for example cyclic codes are ideals in the group ring over a cyclic group. The fresh focus is on the encodings themselves, which only under very limited conditions result in idea...

Central Idempotents in Group Algebras