{"paper":{"title":"Symmetric Implication Zroupoids and Weak Associative Laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Hanamantagouda P. Sankappanavar, Juan M. Cornejo","submitted_at":"2017-10-28T07:29:16Z","abstract_excerpt":"An algebra $\\mathbf A = \\langle A, \\to, 0 \\rangle$, where $\\to$ is binary and $0$ is a constant, is called an implication zroupoid ($\\mathcal I$-zroupoid, for short) if $\\mathbf A$ satisfies the identities: $(x \\to y) \\to z \\approx ((z' \\to x) \\to (y \\to z)')'$ and $0'' \\approx 0$, where $x' : = x \\to 0$. An implication zroupoid is symmetric if it satisfies $x'' \\approx x$ and $(x \\to y')' \\approx (y \\to x')'$. The variety of symmetric $\\mathcal I$-zroupoids is denoted by $\\mathcal S$. We began a systematic analysis of weak associative laws of length $\\leq 4$ in [CS16e], by examining the ident"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10408","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"}