{"paper":{"title":"K_0-theory of n-potents in rings and algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.KT","authors_text":"Efton Park, Jody Trout","submitted_at":"2007-04-05T18:23:47Z","abstract_excerpt":"Let $n \\geq 2$ be an integer. An \\emph{$n$-potent} is an element $e$ of a ring $R$ such that $e^n = e$. In this paper, we study $n$-potents in matrices over $R$ and use them to construct an abelian group $K_0^n(R)$. If $A$ is a complex algebra, there is a group isomorphism $K_0^n(A) \\cong \\bigl(K_0(A)\\bigr)^{n-1}$ for all $n \\geq 2$. However, for algebras over cyclotomic fields, this is not true in general. We consider $K_0^n$ as a covariant functor, and show that it is also functorial for a generalization of homomorphism called an \\emph{$n$-homomorphism}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.0775","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"}