Related papers: Pseudo-Sylvester domains and skew Laurent polynomi…

In this work, free multivariate skew polynomial rings are considered, together with their quotients over ideals of skew polynomials that vanish at every point (which includes minimal multivariate skew polynomial rings). We provide a full…

Building on the work of K. Chiba (J. Algebra 263 (2003), 75-87), we present sufficient conditions for the completion of a division ring with respect to the metric defined by a discrete valuation function to contain a free field, i.e. the…

The main result of this paper is a generalization of the theorem of Chevalley-Shephard-Todd to the rings of invariants of pseudo-reflection groups over regular domains. More precisely, let $A$ be a regular domain and let $K$ be its field of…

Given a ring $R$, the notion of Sylvester rank function was conceived within the context of Cohn's classification theory of epic division $R$-rings. In this paper we study and describe the space of Sylvester rank functions on certain…

Let $G$ be a finitely generated torsion-free pro-$p$ group containing an open free-by-$\mathbb{Z}_p$ pro-$p$ subgroup. We show that the completed group algebra of $G$ over $\mathbb{F}_p$ is a Sylvester domain. Moreover the inner rank of a…

In this paper we proved that if $R$ is right $\omega$-Euclidean domain, then skew Laurent formal series ring is right $\omega$-Euclidean domain. We also showed that if $R$ is a right $\omega$-Euclidean domain with multiplicative norm, then…

Some general criteria to produce explicit free algebras inside the division ring of fractions of skew polynomial rings are presented. These criteria are applied to some special cases of division rings with natural involutions, yielding, for…

Semi-free ideal rings, or semifirs, were introduced by Paul M. Cohn to study universal localizations in the non-commutative setting. We provide new examples of semifirs consisting of analytic functions in several non-commuting variables.…

Let $D$ be a division ring of fractions of a crossed product $F[G,\eta,\alpha]$ where $F$ is a skew field and $G$ is a group with Conradian left-order $\leq$. For $D$ we introduce the notion of freeness with respect to $\leq$ and show that…

In this article, we study skew constacyclic codes over a class of finite commutative semisimple rings. The automorphism group of $\mathcal{R}=\prod_{i=1}^t F_q$ is determined, and we characterize skew constacyclic codes over ring by linear…

The classical Hilbert specialization property is a field-theoretic tool ensuring that polynomial irreducibility over a field is preserved under specialization of some of the variables. We develop an integral counterpart by introducing the…

Let $R$ be a real smooth affine domain of dimension $3$ such that $R$ has either no real maximal ideals or the intersection of all real maximal ideals in $R$ has height at least $1$. Then we prove that all stably free $R$-modules of rank…

Starting with an integral domain $D$ of characteristic $0$, we consider a class of iterated wreath product $W_n$ of $n$ copies of $D$. In order that $W_n$ be transfinite hypercentral, it is necessary to restrict to the case of wreath…

Let $V$ be a rank one valuation domain with quotient field $K$. We characterize the subsets $S$ of $V$ for which the ring of integer-valued polynomials ${\rm Int}(S,V)=\{f\in K[X] \mid f(S)\subseteq V\}$ is a Pr\"ufer domain. The…

Let $ L((T^{-1}))$ be the space of (inverse) Laurent serieswith coefficients in some field $L$. It has a standard degree map and the induced topology. With its usual addition and a new product on this space which is continuous and preserves…

Let k be an algebraically closed field of characteristic zero and let B be a finitely generated k-domain. We study semisimple derivations on B, with special emphasis on those whose eigenvalues are integers. For such derivations, after…

Recently, N. Epstein and J. Shapiro introduced and studied the perinormal domains: those domains A whose going down overrings are flat A-modules. We show that every Pr\"ufer v-multiplication domain is perinormal and has no proper lying over…

Makar-Limanov's conjecture states that if a division ring D is finitely generated and infinite dimensional over its center k then D contains a free k-subalgebra of rank 2. In this work, we will investigate the existence of such structures…

We consider skew free extensions of rings, also known as free multivariate skew polynomial rings, and explore some of the algebraic aspects of this construction. We give different characterizations of such rings and present conditions for…

The notion of symmetry in polynomial rings with several indeterminates is generalized to polynomial rings over finite fields. Families of extensions of the projective line over a finite field of constants possessing this property are…