Related papers: F-schemes
Let R be a commutative ring with identity and M be an R-module. The purpose of this paper is to introduce and investigate the dual notion of morphic modules over a commutative ring.
In this paper we study the ring of global sections of an open subset U=D(I) in Spec A, where A is a two-dimensional noetherian ring. The main concern is to give a geometric criterion when these rings are finitely generated, in order to…
In this paper, we give some categorical description of the general spectrum functor, defining it as an adjoint of a global section functor. The general spectrum functor includes that of $F_1$ and of semirings.
This paper introduces a notion of integrality that is suitable for non-commutative varieties. It is compatible with the usual notion of integrality for schemes. The function field and generic point of a non-commutative integral space are…
We introduce quantum association schemes. This allows to define distance regular and strongly regular quantum graphs. We bring examples thereof. In addition, we formulate the duality for translation quantum association schemes corresponding…
An orthogonal approach to the fuzzification of both multisets and hybrid sets is presented. In particular, we introduce L-multi-fuzzy and L-fuzzy hybrid sets, which are general enough and in spirit with the basic concepts of fuzzy set…
We provide both a general framework for discretizing de Rham sequences of differential forms of high regularity, and some examples of finite element spaces that fit in the framework. The general framework is an extension of the previously…
The main goal of this article is to introduce the concept of $EM-G-$graded rings. This concept is an extension of the notion of $EM-$rings. Let $G$ be a group and $R$ be a $G-$graded commutative ring. The $G-$gradation of $R$ can be…
We introduce and investigate the so-called D-regularly nil clean rings by showing that these rings are, in fact, a non-trivial generalization of the classical von Neumann regular rings and of the strongly $\pi$-regular rings. Some other…
In the present paper, we first describe the principal basis of non-integral geometry. Non-integral geometry is a new field of generalized function (distribution) theory where the effects breaking the symmetry of integration measure have…
In this paper, new and significant advances on the understanding the structure of p.p. rings and their generalizations have been made. Especially among them, it is proved that a commutative ring $R$ is a generalized p.p. ring if and only if…
Let $G$ be a graph and $f: G\rightarrow G$ be a continuous map. We establish a structure theorem which describes the structures of the set $R(f)-\overline{P(f)}$, where $R(f)$ and $P(f)$ are the recurrent point set and the periodic point…
We describe the unitary globalization of cohomologically induced modules $A_{\fq}(\lambda)$. The purpose of the paper is to give a geometric realization of the unitarizable modules. Our results do not constitute a proof of unitarity.
We give a generalization of Poitou-Tate duality to schemes of finite type over rings of integers of global fields.
In the article Categorical Construction of Schemes, arXiv:2511.03433 we gave a natural definition of ordinary schemes based on the fact that the localization of a ring in a maximal ideal is a local representation of the corresponding…
In the paper the notion of {\em Rauzy scheme} is introduced. From Rauzy graph Rauzy Scheme can be obtaining by uniting sequence of vertices of ingoing and outgoing degree 1 by arches. This notion is a tool to describe Rauzy graph behavior.…
Several generalizations of a commutative ring that is a graded complete intersection are proposed for a noncommutative graded $k$-algebra; these notions are justified by examples from noncommutative invariant theory.
This paper is devoted to the open problem in $\mathbb{F}_1$-geometry of developing $K$-theory for $\mathbb{F}_1$-schemes. We provide all necessary facts from the theory of monoid actions on pointed sets and we introduce sheaves for…
We use techniques from relative algebraic geometry and homotopical algebraic geometry in order to construct several categories of schemes defined "under Spec Z". We define this way the categories of N-schemes, F_1-schemes, S-schemes,…
This paper contains a loose collection of remarks on F1-schemes. Etale morphisms and universal coverings are introduced. The relation to toric varieties, at least for integral schemes, is clarified.In this paper it is shown that integral…