Related papers: Power series over generalized Krull domains

We study some generalizations of the notion of regular crossed products K*G. For the case when K is an algebraically closed field, we give necessary and sufficient conditions for the twisted group ring K*G to be an n-weakly regular ring, a…

Let $Q$ be a finite quiver and $\Lambda$ be the radical square zero algebra of $Q$ over a field. We give a full and dense functor from the category of reduced differential projective modules over $\Lambda$ to the category of representations…

Let $D$ be a domain and let $S$ be a torsion-free monoid whose quotient group satisfies the ascending chain condition on cyclic subgroups. We give a characterization of when the monoid algebra $D[S]$ is weakly Krull. As corollaries, we…

Let $K$ be an algebraically closed field of arbitrary characteristic. Let $A$ be an affine domain over $K$ with transcendence degree 1 which is not isomorphic to $K[x]$, and let $B$ be a domain over $K$. We show that the AK invariant…

We give an affirmative answer to the following question by Jarden and Narkiewicz: Is it true that every number field has a finite extension L such that the ring of integers of L is generated by its units (as a ring)? As a part of the proof,…

We give a necessary and sufficient condition for a type of generalized power series to be algebraic over the ring of power series with coefficients in a finite field. This result extend a classical theorem of Huang-Stefanescu.

It is a well-known and easily established fact that every Euclidean domain is also a principal ideal domain. However, the converse statement is not true, and this is usually shown by exhibiting as a counterexample the ring of algebraic…

In 2007, Jarden and Narkiewicz raised the following question: Is it true that each algebraic number field has a finite extension L such that the ring of integers of L is generated by its units (as a ring)? In this article, we answer the…

The Bohr radius for power series of holomorphic functions mapping a multidimensional Reinhardt domain into the convex domain in the complex plane is independent of this convex domain.

We investigate generalized quadratic forms with values in the set of rational integers over quadratic fields. We characterize the real quadratic fields which admit a positive definite binary generalized form of this type representing every…

We study rings over which an analogue of the Weierstrass preparation theorem holds for power series. We show that a commutative ring $R$ admits a factorization of every power series in $R[[x]]$ as the product of a polynomial and a unit if…

Let $H(R, \phi, z)$ be a generalized Weyl algebra associated with a ring $R$, its central element $z\in Z(R)$ and an automorphism $\phi,$ such that for some $l \geq 1$, $\phi^l(z)-z$ is nilpotent and $(z,\phi^i(z))=R$ for all $0<i<l$. We…

Given an integral domain $D$ with quotient field $\mathcal{Q}(D)$, the reciprocal complement of $D$ is the subring $R(D)$ of $\mathcal{Q}(D)$ whose elements are all the sums $\frac{1}{d_1}+\ldots+\frac{1}{d_n} $ for $d_1, \ldots, d_n$…

It was proved in [3] that every h-divisible modules admits an strongly flat cover over all integral domains; and every divisible module over an integral domain R admits a strongly flat cover if and only if R is a Matlis domain. In this…

We show that the compositions of positive integers may be interpreted in terms of powers of some power series, over arbitrary commutative ring. As consequences, several closed formulas for the compositions as well as for the generalized…

We classify all rational maps $H \in K(x)^n$ for which ${\rm trdeg}_K K(tH_1,tH_2,\ldots,tH_n) \le 2$, where $K$ is any field and $t$ is another indeterminate. Furthermore, we classify all such maps for which additionally $JH \cdot H = {\rm…

In the present paper, we investigate the commutativity of quotient ring $R/P$ where $R$ is any ring and $P$ is a prime ideal of $R$ which admits generalized derivations are satisfying some algebraic identities acting on prime ideals $P$.

This is the third paper in a sequence on Krull dimension for limit groups, answering a question of Z. Sela. We give generalizations of the well known fact that a nontrivial commutator in a free group is not a proper power to both graphs of…

We study the "q-commutative" power series ring R:=k_q[[x_1,...,x_n]], defined by the relations x_ix_j = q_{ij}x_j x_i, for multiplicatively antisymmetric scalars q_{ij} in a field k. Our results provide a detailed account of prime ideal…

Suppose that $k$ is an arbitrary field. Consider the field $k((x_1,...,x_n))$, which is the quotient field of the ring $k[[x_1,...,x_n]]$ of formal power series in the variables $x_1,...,x_n$, with coefficients in $k$. Suppose that $\sigma$…