Local derivations in polynomial and power series rings

Group Actions on Polynomial and Power Series Rings

Standard bases in mixed power series and polynomial rings over rings

In this paper we study standard bases for submodules of a mixed power series and polynomial ring RJt1, . . . , tmK[x1, . . . , xn] s respectively of their localization with respect to a t-local monomial ordering for a certain class of noetherian rings R. The main steps are to prove the existence of a division with remainder generalizing and combining the division theorems of Grauert–Hironaka an...

Convergent Higher Derivations on Local Rings

Derivations in semiprime rings and Banach algebras

Let $R$ be a 2-torsion free semiprime ring with extended centroid $C$, $U$ the Utumi quotient ring of $R$ and $m,n>0$ are fixed integers. We show that if $R$ admits derivation $d$ such that $b[[d(x), x]_n,[y,d(y)]_m]=0$ for all $x,yin R$ where $0neq bin R$, then there exists a central idempotent element $e$ of $U$ such that $eU$ is commutative ring and $d$ induce a zero derivation on $(1-e)U$. ...

Anti-archimedean Rings and Power Series Rings

We define an integral domain D to be anti-Archimedean if ⋂∞ n=1 a nD 6= 0 for each 0 6= a ∈ D. For example, a valuation domain or SFT Prüfer domain is anti-Archimedean if and only if it has no height-one prime ideals. A number of constructions and stability results for anti-Archimedean domains are given. We show that D is anti-Archimedean ⇔ D[[X1, . . .