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arXiv · 1601.01395

Classification of modules over laterally complete regular algebras

Vladimir I. Chilin·Jasurbek A. Karimov
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Abstract

Let $\mathcal{A}$ be a laterally complete commutative regular algebra and $X$ be a laterally complete $\mathcal{A}$-module. In this paper we introduce a notion of passport $Γ(X)$ for $X$, which consist of uniquely defined partition of unity in the Boolean algebra of idempotents in $\mathcal{A}$ and the set of pairwise different cardinal numbers. It is proved that $\mathcal{A}$-modules $X$ and $Y$ are isomorphic if and only if $Γ(X) = Γ(Y)$.

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Vladimir I. Chilin, Jasurbek A. Karimov. 2016-01-07. Classification of modules over laterally complete regular algebras. https://arxiv.org/abs/1601.01395

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