6 problems

Let $\alpha,\beta\models_0 n$ be compositions, let $\mathcal{C}_{\alpha,\beta}$ be the associated collection, and define … Let $L_{\alpha,\beta}\in R_{\alpha,\beta}$ be the linear…

Bavula's quotient-ring conjecture. There is an isomorphism

Inductive-limit isomorphism conjecture. The ring $\widehat{\mathbb{Z}}$ is isomorphic to $\mathbb{Z}/\infty\mathbb{Z}$.

Uniqueness conjecture. The limit $(\mathbb{Z}/\infty\mathbb{Z},\tilde{d}_{\infty})$ is unique for arbitrary Dirichlet arithmetic progressions.

Let $K$ be a field of zero characteristic, let $A_n=K\langle x_1,\ldots,x_n,\frac{\partial}{\partial x_1},\ldots,\frac{\partial}{\partial x_n}\rangle$ be the Weyl algebra, and let…

Let $S=\Bbbk[x_{1},\ldots,x_{n}]$, let $P=(x_{1}^{e_{1}},\ldots,x_{r}^{e_{r}})$, and set $R=S/P$. Let $I$ be a homogeneous ideal containing $P$, and let $L$ be the lex-plus-$P$ ide…