6 problems

Let $D$ be an integral domain, and let $R(D)$ denote its reciprocal complement, the subring generated by the inverses of all nonzero elements of $D$. Dimension conjecture. For any…

Finite-Krull-dimension conjecture. The following assertions hold:

Krull-dimension conjecture. The inequality

Let $M$ be a closed, oriented, smooth manifold that is positively rationally elliptic and satisfies the Halperin conjecture. Let $\hat{A}(M)$ denote its $\mathop{\hat{A}}$-genus, l…

Let GCH denote the assertion that for every infinite cardinal $\kappa$, there is no cardinal properly between $\kappa$ and $2^\kappa$. For an infinite cardinal number $\kappa$, let…

Graphical-dimension conjecture. The Krull dimension of $\bar{A}(G)$ is equal to the graphical dimension of $G$.