Gröbner-nice pairs of ideals
We introduce the concept of a Gröbner nice pair of ideals in a polynomial ring and we present some applications.
math.AC↗
arXiv subjects
Mircea Cimpoeaş
Publications and source records attributed to Mircea Cimpoeaş.
On the algebraic properties of the ring of Dirichlet convolutions
Let $R$ be a commutative ring and $Γ$ a commutative monoid of finite type. We study algebraic properties of modules and derivations over the associated ring $\mathcal F(Γ,R)$ of Dirichlet convolutions. If $Γ$ is cancellative and $G(Γ)$ is its associated Grothendieck group, we construct a natural extension $\mathcal F^f(G(Γ),R)$ of $\mathcal F(Γ,R)$ and we study its basic properties. Further properties are discussed in the case $Γ=\mathbb N^*$ and $G(Γ)=\mathbb Q^*_+$. In particular, we show that $\mathcal F^f(\mathbb Q^*_+,R)\cong R[[x_1,x_2,\ldots,]][x_1^{-1},x_2^{-1},\ldots]$.
math.AC↗