Torsion-free soluble groups, completions, and the zero divisor conjecture

Torsion in Profinite Completions of Torsion-free Groups

LET G be a residually-finite torsion-free group. Is Gthe profinite completion of G-torsion free? This question was asked in [CKL] where it was shown that if G is a finitely generated metabelian-by-finite group then indeed G is torsion free. On the other hand Evans [E] showed that if G is not finitely generated then it is possible that G has torsion. His example is also metabelian. In this note ...

$C_4$-free zero-divisor graphs

‎In this paper we give a characterization for all commutative‎ ‎rings with $1$ whose zero-divisor graphs are $C_4$-free.‎

$c_4$-free zero-divisor graphs

‎in this paper we give a characterization for all commutative‎ ‎rings with $1$ whose zero-divisor graphs are $c_4$-free.‎

On the analytic zero divisor conjecture of Linnell

In this note we prove that in the case of finitely generated amenable groups the classical zero divisor conjecture implies the analytic zero divisor conjecture of Linnell.

The HRT Conjecture and the Zero Divisor Conjecture for the Heisenberg Group