6 problems

Let $R$ be a commutative ring, let $I$ be an $n$-absorbing ideal of $R$, and let $R[X]$ and $I[X]$ denote the polynomial ring and the extended ideal, respectively. Anderson–Badawi'…

Let a naturally occurring class of graded $n$-absorbing ideals be given, together with a combinatorial parameter space whose vertices, geometric positions, strata, and faces may en…

Graded-ring conjecture. For any ideal $\alpha$ of a graded ring $R$,

Polynomial-extension conjecture. The maximal collections of $\alpha[x]$ are of the form $M[x]$ for some maximal collection $M=[M_i]_i$ of $\alpha$.

Finiteness conjecture. Every ideal of a Noetherian ring has finitely many maximal collections.

Power-series extension conjecture. For every ideal $I$ of $R$,