{"paper":{"title":"$z^\\circ$-ideals in intermediate rings of ordered field valued continuous functions","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Dhananjoy Mandal, Sagarmoy Bag, Sudip Kumar Acharyya","submitted_at":"2017-12-22T06:15:31Z","abstract_excerpt":"A proper ideal $I$ in a commutative ring with unity is called a $z^\\circ$-ideal if for each $a$ in $I$, the intersection of all minimal prime ideals in $R$ which contain $a$ is contained in $I$. For any totally ordered field $F$ and a completely $F$-regular topological space $X$, let $C(X,F)$ be the ring of all $F$-valued continuous functions on $X$ and $B(X,F)$ the aggregate of all those functions which are bounded over $X$. An explicit formula for all the $z^\\circ$-ideals in $A(X,F)$ in terms of ideals of closed sets in $X$ is given. It turns out that an intermediate ring $A(X,F)\\neq C(X,F)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08312","kind":"arxiv","version":1},"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"}