Positive rigs

IF 1 3区数学 Q1 MATHEMATICS

Forum Mathematicum Pub Date : 2023-11-29 DOI:10.1515/forum-2022-0271

Matías Menni

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引用次数: 0

Abstract

A positive rig is a commutative and unitary semi-ring A such that 1 + x

{1+x}

is invertible for every x ∈ A

{x\in A}

. We show that the category of positive rigs shares many properties with that of K-algebras for a (non-algebraically closed) field K. In particular, it is coextensive and, although we do not have an analogue of Hilbert’s basis theorem for positive rigs, we show that every finitely presentable positive rig is a finite direct product of directly indecomposable ones. We also describe free positive rigs as rigs of rational functions with non-negative rational coefficients, and we give a characterization of the positive rigs with a unique maximal ideal.

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积极的钻井平台

正对是一个交换酉半环A，使得1+x {1+x}对A中的每一个x∈A {x\in A}可逆。我们证明了正钻机的范畴与k -代数的范畴在(非代数闭)域k上具有许多相同的性质，特别是，它是共扩展的，尽管我们没有关于正钻机的希尔伯特基定理的类似物，但我们证明了每一个有限可呈现的正钻机都是直接不可分解的有限直接积。我们还将自由正钻机描述为具有非负有理系数的有理函数钻机，并给出了具有唯一极大理想的正钻机的表征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Forum Mathematicum 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Forum Mathematicum is a general mathematics journal, which is devoted to the publication of research articles in all fields of pure and applied mathematics, including mathematical physics. Forum Mathematicum belongs to the top 50 journals in pure and applied mathematics, as measured by citation impact.