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Main Author: Nasehpour, Peyman
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2508.01471
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author Nasehpour, Peyman
author_facet Nasehpour, Peyman
contents In the second section, we introduce hemiring-valued pseudonormed rings and generalize Albert's result which states that every finite-dimensional algebra can be normed. Next, we introduce shrinkable hemirings and prove that dense division semirings are shrinkable. In the third section, we show the Cauchy Condensation Test holds for Cauchy complete fields. In the fourth section, we use Bernoulli's inequality to prove a version of ratio test for ring-valued normed groups.
format Preprint
id arxiv_https___arxiv_org_abs_2508_01471
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Hemiring-valued pseudonormed rings
Nasehpour, Peyman
Commutative Algebra
Rings and Algebras
06F25, 16Y60, 40A05, 40J05
In the second section, we introduce hemiring-valued pseudonormed rings and generalize Albert's result which states that every finite-dimensional algebra can be normed. Next, we introduce shrinkable hemirings and prove that dense division semirings are shrinkable. In the third section, we show the Cauchy Condensation Test holds for Cauchy complete fields. In the fourth section, we use Bernoulli's inequality to prove a version of ratio test for ring-valued normed groups.
title Hemiring-valued pseudonormed rings
topic Commutative Algebra
Rings and Algebras
06F25, 16Y60, 40A05, 40J05
url https://arxiv.org/abs/2508.01471