In mathematics, the field with one element is a suggestive name for an object that should behave similarly to a finite field with a single element, ... History · Expected properties · Monoid schemes

9 апр. 2024 г. · While there is no field with a single element in the standard sense of field, the idea is that there is some other object, denoted 𝔽 1 \mathbb{F}_ ... Function field analogy · Algebra over 𝔽 1 \mathbb{F}_1

24 окт. 2009 г. · There's no field with one element in the literal sense, but there are constructions that work over different fields Fq and which sometimes make ... Inter-Universal Teichmuller Theory and the Field with One ... Étale cohomology of the field with one element - MathOverflow Другие результаты с сайта mathoverflow.net

11 окт. 2017 г. · The field with one element is a conjectured object in mathematics which would appear as a degenerate case in a number of technical situations ... What's the point of discussion about the field with one element ... Help me understand F1, 'the (non-existent) field with one element' Другие результаты с сайта www.reddit.com

6 дек. 2020 г. · One of the axioms of the field is that 0≠1. This is part of the definition. We don't want the {0} ring to be a field. What is "Field with One Element"? - Math Stack Exchange Examples of fields of characteristic 1 - Math Stack Exchange Field with one element in an elementary context Why isn't the zero ring the field with one element? Другие результаты с сайта math.stackexchange.com

20 июл. 2011 г. · There is no “field with one element”: every field has at least two elements. Thus, the field with one element is essentially a poetic concept.

8 дек. 2023 г. · The field with one element, F1 F 1 , is a nonexistent mathematical concept (fields are supposed to contain at least two distinct elements, 0 and ...

In 1957, Tits [1] proposed to think of W as the group of points of G in "the field of characteristic one": (1) G(F1) := W. He also argued that the finite ...

17 апр. 2007 г. · The field with one element is the algebraic theory with one nullary constant and nothing else, whose algebras are obviously pointed sets.

17 июн. 2009 г. · We show that Lambda-algebraic geometry is in a precise sense an algebraic geometry over a deeper base than Z and that it has many properties ...