Abstract:We introduce the overflow semiring $S = A \oplus_{\operatorname{ord}} L$, extending a positive information algebra $A$ by a join-semilattice $L$, where elements of $L$ dominate $A$ and arithmetic in $L$ reduces to the join. This models saturation or overflow in computational systems and generalizes the transition from finite to infinite cardinal arithmetic. We characterize the idempotent elements of $S$ and $S[X]$, fully classify idempotent power series over cardinal numbers, describe the structure of prime and maximal ideals, compute the Krull dimension of $S$ ($\dim S = \dim A + |L|$ for well-ordered finite $L$), and establish Noetherian and Artinian criteria.
From: Peyman Nasehpour [view email]
[v1]
Sat, 30 May 2026 22:50:50 UTC (20 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。