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arXiv · 0704.0775

K_0-theory of n-potents in rings and algebras

Efton Park·Jody Trout
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Abstract

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}.

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Efton Park, Jody Trout. 2018-09-06. K_0-theory of n-potents in rings and algebras. https://arxiv.org/abs/0704.0775

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