N. J. Werner · wovepaper

activity

20142026

most citedProperly Integral Polynomials over the Ring of Integer-valued Polynomials on a Matrix Ring

17 citations · 52 across the 12 of their papers we have counts for

collaborators

15 papers

Some results on null ideals of finite rings

Nicholas J. Werner

For a finite associative unital ring $R$ , the null ideal of $R$ is the collection of polynomials with coefficients from $R$ that send each element of $R$ to zero under evaluation.…

A classification of Prufer domains of integer-valued polynomials on algebras

Giulio Peruginelli, Nicholas J. Werner

Let $D$ be an integrally closed domain with quotient field $K$ and $A$ a torsion-free $D$ -algebra that is finitely generated as a $D$ -module and such that $A \cap K = D$ . We give a co…

Integer-valued polynomials on subsets of quaternion algebras

Nicholas J. Werner

Let $R$ be either the ring of Lipschitz quaternions, or the ring of Hurwitz quaternions. Then, $R$ is a subring of the division ring $D$ of rational quaternions. For $S \s…

Nontriviality of rings of integral-valued polynomials

Giulio Peruginelli, Nicholas J. Werner

Let $S$ be a subset of $Z$ , the ring of all algebraic integers. A polynomial $f \in Q [X]$ is said to be integral-valued on $S$ if $f(s) \in \overline{\ma…

Counting core sets in matrix rings over finite fields

Roswitha Rissner, Nicholas J. Werner

Let $R$ be a commutative ring and $M_{n} (R)$ be the ring of $n \times n$ matrices with entries from $R$ . For each $S \subseteq M_{n} (R)$ , we consider its (generalized) null ideal $N(S)…

Null ideals of sets of $3 \times 3$ similar matrices with irreducible characteristic polynomial

Eric Swartz, Nicholas J. Werner

Let $F$ be a field and $M_{n} (F)$ the ring of $n \times n$ matrices over $F$ . Given a subset $S$ of $M_{n} (F)$ , the null ideal of $S$ is the set of all polynomials $f$ with coefficient…

A new infinite family of $σ$ -elementary rings

Eric Swartz, Nicholas J. Werner

A cover of an associative (not necessarily commutative nor unital) ring $R$ is a collection of proper subrings of $R$ whose set-theoretic union equals $R$ . If such a cover exists,…

The covering numbers of rings

Eric Swartz, Nicholas J. Werner

A cover of an associative (not necessarily commutative nor unital) ring $R$ is a collection of proper subrings of $R$ whose set-theoretic union equals $R$ . If such a cover exists,…

Covering numbers of commutative rings

Eric Swartz, Nicholas J. Werner

A cover of a unital, associative (not necessarily commutative) ring $R$ is a collection of proper subrings of $R$ whose set-theoretic union equals $R$ . If such a cover exists, then…

Fuchs' problem for 2-groups

Eric Swartz, Nicholas J. Werner

Nearly $60$ years ago, László Fuchs posed the problem of determining which groups can be realized as the group of units of a commutative ring. To date, the question remains open, a…

On the number of reachable pairs in a digraph

Eric Swartz, Nicholas J. Werner

A pair $(u, v)$ of (not necessarily distinct) vertices in a directed graph $D$ is called a reachable pair if there exists a directed path from $u$ to $v$ . We define the weight of $…

math.RA2016★ 8 cited

Decomposition of integer-valued polynomial algebras

Giulio Peruginelli, Nicholas J. Werner

Let $D$ be a commutative domain with field of fractions $K$ , let $A$ be a torsion-free $D$ -algebra, and let $B$ be the extension of $A$ to a $K$ -algebra. The set of integer-valued…

math.RA2016★ 12 cited

Non-triviality Conditions for Integer-valued Polynomial Rings on Algebras

G. Peruginelli, N. J. Werner

Let $D$ be a commutative domain with field of fractions $K$ and let $A$ be a torsion-free $D$ -algebra such that $A \cap K = D$ . The ring of integer-valued polynomials on $A$ with c…

math.RA2015★ 17 cited

Properly Integral Polynomials over the Ring of Integer-valued Polynomials on a Matrix Ring

Giulio Peruginelli, Nicholas J. Werner

Let $D$ be a domain with fraction field $K$ , and let $M_{n} (D)$ be the ring of $n \times n$ matrices with entries in $D$ . The ring of integer-valued polynomials on the matrix ring $M…

math.AC2014★ 15 cited

Integral closure of rings of integer-valued polynomials on algebras

Giulio Peruginelli, Nicholas J. Werner

Let $D$ be an integrally closed domain with quotient field $K$ . Let $A$ be a torsion-free $D$ -algebra that is finitely generated as a $D$ -module. For every $a$ in $A$ we consider i…