Related papers: Intermediate algebras of semialgebraic functions

In a previous article by two of the present authors and S. Bonzio, \L ukasiewicz near semirings were introduced and it was proven that basic algebras can be represented (precisely, are term equivalent to) as near semirings. In the same work…

For an algebraically closed field K, let G be a finite abelian group of K-linear automorphisms of a finite-dimensional algebra A and AG is the associated skew group algebra. The author with S. Trepode and A. G. Chaio introduced the notion…

We characterize all semigroups sandwiched between the semigroup of a Dirichlet form and the semigroup of its active main part. In case the Dirichlet form is regular, we give a more explicit description of the quadratic forms of the…

We define a Grothendieck ring for basic real semialgebraic formulas, that is for systems of real algebraic equations and inequalities. In this ring the class of a formula takes into consideration the algebraic nature of the set of points…

Given an ideal $\mathfrak{a}$ in $A[x_1, \ldots, x_n]$, where $A$ is a Noetherian integral domain, we propose an approach to compute the Krull dimension of $A[x_1,\ldots,x_n]/\mathfrak{a}$, when the residue class polynomial ring is a free…

Let $K$ be a number field with ring of integers $R$. Given a modulus $\mathfrak{m}$ for $K$ and a group $\Gamma$ of residues modulo $\mathfrak{m}$, we consider the semi-direct product $R\rtimes R_{\mathfrak{m},\Gamma}$ obtained by…

Intermediate rings of real valued continuous functions with countable range on a Hausdorff zero-dimensional space $X$ are introduced in this article. Let $\Sigma_c(X)$ be the family of all such intermediate rings $A_c(X)$'s which lie…

We present constructive versions of Krull's dimension theory for commutative rings and distributive lattices. The foundations of these constructive versions are due to Joyal, Espa\~nol and the authors. We show that the notion of Krull…

The norm closure of the algebra generated by the set $\{n\mapsto {\lambda}^{n^k}:$ $\lambda\in{\mathbb {T}}$ and $k\in{\mathbb{N}}\}$ of functions on $({\mathbb {Z}}, +)$ was studied in \cite{S} (and was named as the Weyl algebra). In this…

We set up a left ring of fractions over a certain ring of boundary problems for linear ordinary differential equations. The fraction ring acts naturally on a new module of generalized functions. The latter includes an isomorphic copy of the…

We define and study large and stably large subalgebras of simple unital C*-algebras. The basic example is the orbit breaking subalgebra of a crossed product by Z, as follows. Let X be an infinite compact metric space, let h be a minimal…

Given a closed ideal I in a C*-algebra A, an ideal J (not necessarily closed) in I, a *-homomorphism \al:A --> M(I) and a map L:J --> A with some properties, based on [3] and [9] we define a C*-algebra O(A,\al,L) which we call the "Crossed…

We prove that cellular Noetherian algebras with finite global dimension are split quasi-hereditary over a regular commutative Noetherian ring with finite Krull dimension and their quasi-hereditary structure is unique, up to equivalence. In…

In this work we prove that a semialgebraic set $M\subset{\mathbb R}^m$ is determined (up to a semialgebraic homeomorphism) by its ring ${\mathcal S}(M)$ of (continuous) semialgebraic functions while its ring ${\mathcal S}^*(M)$ of…

We develop a new technique for studying monomial ideals in the standard polynomial rings $A[X_1,\ldots,X_d]$ where $A$ is a commutative ring with identity. The main idea is to consider induced ideals in the semigroup ring…

In this paper semirings with an idempotent addition are considered. These algebraic structures are endowed with a partial order. This allows to consider residuated maps to solve systems of inequalities $A \otimes X \preceq B$. The purpose…

Let $X$ be an $n\times m$ matrix of indeterminates over a field $K$ (of sufficiently large characteristic) and $M_t$ the set of $m$-minors of $X$. We consider two objects: (1) the Ress algebra of the polynomial ring $K[X]$ with respect to…

We associate with the ring $R$ of algebraic integers in a number field a C*-algebra $\cT[R]$. It is an extension of the ring C*-algebra $\cA[R]$ studied previously by the first named author in collaboration with X.Li. In contrast to…

In this paper, we introduce and study two new classes of commutative rings, namely semi transitional rings and transitional rings, which extend several classical ideas arising from rings of continuous functions and their variants. A general…

Let $\mathcal{A}$ be an arbitrary hereditary abelian category that may not have enough projective objects. For example, $\mathcal{A}$ can be the category of finite-dimensional representations of a quiver or the category of coherent sheaves…