5 problems

Let $\Lambda$ be a special biserial algebra, and let $\mathrm{st}(\Lambda)$ denote its stable rank, the ordinal at which the descending powers of the radical stabilize. A special b…

Let $\Lambda$ be a special biserial algebra over an algebraically closed field, and let $\mathrm{st}(\Lambda)$ be the least ordinal at which the decreasing sequence of powers of th…

Let $\Lambda$ be a special biserial algebra with at least one band, and let $\mathrm{st}(\Lambda)$ denote its stable rank. Stable-rank conjecture. The stable rank satisfies … This…

Finitistic-dimension conjecture. The big finitistic dimension satisfies

One-point-extension conjecture. For any monomial relation algebra and any special biserial algebra $\Lambda$, there exists a sequence of one-point extensions