关于两个代数集合的结合何时是代数集合

IF 0.9 3区数学 Q2 MATHEMATICS

Aequationes Mathematicae Pub Date : 2024-04-26 DOI:10.1007/s00010-024-01041-9

Erhard Aichinger, Mike Behrisch, Bernardo Rossi

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引用次数: 0

摘要

在普遍代数几何中，如果两个代数集合的结合是代数的，那么这个代数就叫做等域。我们描述了所有大小为二的代数代数和所有大小为三的具有循环自动形的代数中，关于多项式方程、全等可变品种内的等域，以及关于项方程的等域。此外，对于每种至少为三的大小，我们都证明了在项等价的模态下，存在着该大小的等价域的连续体。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

On when the union of two algebraic sets is algebraic

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On when the union of two algebraic sets is algebraic

In universal algebraic geometry, an algebra is called an equational domain if the union of two algebraic sets is algebraic. We characterize equational domains, with respect to polynomial equations, inside congruence permutable varieties, and with respect to term equations, among all algebras of size two and all algebras of size three with a cyclic automorphism. Furthermore, for each size at least three, we prove that, modulo term equivalence, there is a continuum of equational domains of that size.

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来源期刊

Aequationes Mathematicae MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.70

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： aequationes mathematicae is an international journal of pure and applied mathematics, which emphasizes functional equations, dynamical systems, iteration theory, combinatorics, and geometry. The journal publishes research papers, reports of meetings, and bibliographies. High quality survey articles are an especially welcome feature. In addition, summaries of recent developments and research in the field are published rapidly.