{"paper":{"title":"The composition series of ideals of the partial-isometric crossed product by semigroup of endomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Saeid Zahmatkesh, Sriwulan Adji","submitted_at":"2015-04-16T02:07:19Z","abstract_excerpt":"Let $\\Gamma^{+}$ be the positive cone in a totally ordered abelian group $\\Gamma$, and $\\alpha$ an action of $\\Gamma^{+}$ by extendible endomorphisms of a $C^{\\ast}$-algebra $A$. Suppose $I$ is an extendible $\\alpha$-invariant ideal of $A$. We prove that the partial-isometric crossed product $\\mathcal{I}:=I\\times_{\\alpha}^{\\textrm{piso}}\\Gamma^{+}$ embeds naturally as an ideal of $A\\times_{\\alpha}^{\\textrm{piso}}\\Gamma^{+}$, such that the quotient is the partial-isometric crossed product of the quotient algebra. We claim that this ideal $\\mathcal{I}$ together with the kernel of a natural homom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04083","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"}