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pro vyhledávání: '"Werner, Nicholas J."'
Autor:
Werner, Nicholas J.
Let $R$ be either the ring of Lipschitz quaternions, or the ring of Hurwitz quaternions. Then, $R$ is a subring of the division ring $\mathbb{D}$ of rational quaternions. For $S \subseteq R$, we study the collection $\rm{Int}(S,R) = \{f \in \mathbb{D
Externí odkaz:
http://arxiv.org/abs/2412.20609
Autor:
Swartz, Eric, Werner, Nicholas J.
Sabatini (2024) defined a subgroup $H$ of $G$ to be an exponential subgroup if $x^{|G:H|} \in H$ for all $x \in G$. Exponential subgroups are a generalization of normal (and subnormal) subgroups: all subnormal subgroups are exponential, but not conve
Externí odkaz:
http://arxiv.org/abs/2407.14442
Let $S$ be a subset of $\overline{\mathbb Z}$, the ring of all algebraic integers. A polynomial $f \in \mathbb Q[X]$ is said to be integral-valued on $S$ if $f(s) \in \overline{\mathbb Z}$ for all $s \in S$. The set $\text{Int}_{\mathbb Q}(S,\overlin
Externí odkaz:
http://arxiv.org/abs/2407.09351
Autor:
Werner, Nicholas J.
It is well known that if $G$ is a group and $H$ is a normal subgroup of $G$ of finite index $k$, then $x^k \in H$ for every $x \in G$. We examine finite groups $G$ with the property that $x^k \in H$ for every subgroup $H$ of $G$, where $k$ is the ind
Externí odkaz:
http://arxiv.org/abs/2407.05498
Autor:
Rissner, Roswitha, Werner, Nicholas J.
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 $N(S)$, which is the set of all polynomials $f$ with coefficients from $M_n
Externí odkaz:
http://arxiv.org/abs/2405.04106
Autor:
Swartz, Eric, Werner, Nicholas J.
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 coefficients from $M_n(F)$ such that $f(A) = 0$ for all $A \in S$. We say that $S
Externí odkaz:
http://arxiv.org/abs/2212.14460
Autor:
Swartz, Eric, Werner, Nicholas J.
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, then the covering number $\sigma(R)$ of $R$ is the cardinality of a mi
Externí odkaz:
http://arxiv.org/abs/2211.10313
Autor:
Swartz, Eric, Werner, Nicholas J.
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, then the covering number $\sigma(R)$ of $R$ is the cardinality of a mi
Externí odkaz:
http://arxiv.org/abs/2112.01667
Autor:
Swartz, Eric, Werner, Nicholas J.
Publikováno v:
In Journal of Algebra 1 February 2024 639:249-280
Autor:
Swartz, Eric, Werner, Nicholas J.
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 the covering number $\sigma(R)$ of $R$ is the cardinality of a minima
Externí odkaz:
http://arxiv.org/abs/2008.13218