Related papers: Scheme theory for commutative semirings
In this paper, we give semiring version of some classical results in commutative algebra related to Euclidean rings, PIDs, UFDs, G-domains, and GCD and integrally closed domains.
In this paper we study injective modules over universal enveloping algebras of finite-dimensional Lie algebras over fields of arbitrary characteristic. Most of our results are dealing with fields of prime characteristic but we also…
Let $R$ be a commutative ring with. The purpose of this paper is to introduce and investigate cubes-difference factor absorbing ideals of R as a generalization of prime ideals.
We investigate invertible matrices over finite additively idempotent semirings. The main result provides a criterion for the invertibility of such matrices. We also give a construction of the inverse matrix and a formula for the number of…
A theory of double affine and special double affine bundles, i.e. differential manifolds with two compatible (special) affine bundle structures, is developed as an affine counterpart of the theory of double vector bundles. The motivation…
In this paper, we study the linear transformation model in the most general setup. This model includes many important and popular models in statistics and econometrics as special cases. Although it has been studied for many years, the…
We present two methods to algorithmically compute both least and greatest solutions of polynomial equation systems over absorptive semirings (with certain completeness and continuity assumptions), such as the tropical semiring. Both methods…
In the authors book, Associative Algebraic Geometry, 2023, and the following article Shemes of Associative Algebras,\\ https://doi.org/10.48550/arXiv.2410.17703,2024, we use an algebraization of the semi-local formal moduli of simple…
Let R be a semiring. We say that a non-zero subsemimodule S of an R-semimodule M is second if for each a \in R, we have aS = S or aS = 0. The aim of this paper is to study the notion of second subsemimodules of semimodules over commutative…
Let R be a commutative ring and let Spec(R) denote the collection of prime ideals of R. We define a topology on Spec(R) by using ultrafilters and demonstrate that this topology is identical to the well known patch or constructible topology.…
In this paper, we will introduce the notion of (u,v)-absorbing hyperideals in multiplicative hyperrings and we will show some properties of them. Then we extend this concept to the notion of (u,v)-absorbing prime hyperideals and thhen we…
This paper presents an iterative method suitable for inverting semilinear problems which are important kernels in many numerical applications. The primary idea is to employ a parametrization that is able to reduce semilinear problems into…
This article discusses a way for uniquely setting up the valuations for the minimal generators of the maximal ideal of a one dimensional complete reduced and irreducible local algebra over an algebraically closed field, when treated as a…
This paper focuses on distributive uninorms, which induce structures of commutative ordered semirings. We will show that the second uninorm must be locally internal on $A(e)$, and will present a complete characterization of the structure of…
This paper develops the structural and spectral foundations of noncommutative and n-ary Gamma semirings, extending the commutative ternary framework established in earlier studies. We introduce left, right, and two-sided ideals in the…
We give an account on what is known on the subject of permutation matchings, which are bijections of a finite regular semigroup that map each element to one of its inverses. This includes partial solutions to some open questions, including…
We give an algorithm for computing the factor ring of a given ideal in a Dedekind domain with finite rank, which runs in deterministic and polynomial-time. We provide two applications of the algorithm: judging whether a given ideal is prime…
The main purpose of this paper is to investigate the zero-divisors of semigroups with zero and semirings and in particular, to discuss eversible and reversible semigroups and semirings. We also introduce a new ring-like algebraic structure…
In this paper we introduce prime fuzzy ideals over a noncommutative ring. This notion of primeness is equivalent to level cuts being crisp prime ideals. It also generalizes the one provided by Kumbhojkar and Bapat in [Not-so-fuzzy fuzzy…
In this article, we give a proof for a geometric presentation theorem for any irreducible scheme $X$ smooth projective over a discrete valuation ring $R$. As a consequence, for any reductive $R$-group scheme $\mathbf{G}$, we prove that any…