{"paper":{"title":"The Monoid Structure on Homotopy Obstructions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Bibekananda Mishra, Satya Mandal","submitted_at":"2016-12-02T17:04:13Z","abstract_excerpt":"Let $A$ be a commutative noetherian ring, containing a field $k$, with $1/2\\in k$, $\\dim A=d$, and let $P$ be a projective $A$-module or $rank(P)=n$. In continuation of \\cite{MM}, we study Homotopy obstructions for $P$ to split off a free direct summand. Let ${\\mathcal LO}(P)$ be the set of all pairs $(I, \\omega)$, where $I$ is an ideal of $A$ and $\\omega: P\\rightarrow I/I^2$ is a surjective map. The homotopy relations on ${\\mathcal LO}(P)$, induced by ${\\mathcal LO}(P[T])$, leads to a set $\\pi_0\\left({\\mathcal LO}(P)\\right)$ of equivalence classes in ${\\mathcal LO}(P)$. There are two distingu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00749","kind":"arxiv","version":5},"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"}