{"paper":{"title":"Computing $J$-ideals of a matrix over a principal ideal domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Clemens Heuberger, Roswitha Rissner","submitted_at":"2016-11-30T18:53:58Z","abstract_excerpt":"Given a square matrix $B$ over a principal ideal domain $D$ and an ideal $J$ of $D$, the $J$-ideal of $B$ consists of the polynomials $f\\in D[X]$ such that all entries of $f(B)$ are in $J$. It has been shown that in order to determine all $J$-ideals of $B$ it suffices to compute a generating set of the $(p^t)$-ideal of $B$ for finitely many prime powers $p^t$. Moreover, it is known that $(p^t)$-ideals are generated by polynomials of the form $p^{t-s}\\nu_s$ where $\\nu_s$ is a monic polynomial of minimal degree in the $(p^s)$-ideal of $B$ for some $s\\le t$. However, except for the case of diagon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.10308","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}