8 problems

Let $\mathbb{k}$ be an integral domain with unity and let $X$ be a semi-latin quandle, meaning a quandle whose left and right translations satisfy the relevant latin-type condition…

Let $R$ be a standard graded algebra, and let $d>0$. A pair $(\ell,Q)$ of exact zero divisors means that $\ell$ is a general linear form, $Q$ is an element of degree $d-1$, and the…

Let $R=bigoplus{n i G}Rn$ be a ring graded by a torsion-free group $G$, and let $I$ be a left ideal of $R$. The ideal $I$ is unfaithful when its annihilator is nonzero. **The g…

Pattern-preserving weak equivalence conjecture. The embedding $\mathcal I$ is a weak homotopy equivalence.

Let $G$ be a group, let $\mathbb C G$ be its complex group algebra, and let $\ell^2(G)$ be the Hilbert-space completion of $\mathbb C G$ in the 2-norm. Linnell's analytic zero divi…

Let $\Bbbk$ be a field of characteristic zero and let $G$ be a torsion-free group. An idempotent in the group ring $\Bbbk[G]$ is an element $p$ satisfying $p^2=p$. The trivial idem…

Let $G$ be a torsion-free group and let $R$ be an integral domain. A non-trivial zero divisor in the group ring $R[G]$ is a nonzero element $\alpha\in R[G]$ for which there exists…

Let $K$ be a division ring and let $G$ be a group. The Zero Divisors Conjecture. If $K[G]$ contains zero divisors, then $G$ has torsion. The source states that the Invertibles Conj…