Related papers: S-Noetherian generalized power series rings

A ring $R$ is called a left APP-ring if the left annihilator $l_{R}(Ra)$ is right $s$-unital as an ideal of $R$ for any $a\in R$. Let $R$ be a ring, $(S,\leq)$ a strictly ordered monoid and $\omega:S\longrightarrow {\rm End}(R)$ a monoid…

Let $R$ be a ring, $(S,\preceq)$ a strictly totally ordered monoid and suppose also $\omega:S\rightarrow \text{End}(R)$ is a monoid homomorphism. A skew generalized power series ring $R[[S,\omega,\preceq]]$ consists of all functions from a…

We study skew inverse power series extensions R[[y^{-1};tau,delta]], where R is a noetherian ring equipped with an automorphism tau and a tau-derivation delta. We find that these extensions share many of the well known features of…

We study prime ideals in skew power series rings $T:=R[[y;\tau,\delta]]$, for suitably conditioned right noetherian complete semilocal rings $R$, automorphisms $\tau$ of $R$, and $\tau$-derivations $\delta$ of $R$. These rings were…

Let $R$ be a ring, $(S,\leq)$ a strictly ordered monoid and $\omega: S\rightarrow End(R)$ a monoid homomorphism. In this paper we study the ascending chain conditions on principal left (resp. right) ideals of the skew generalized power…

Let $R$ be a ring with identity, $(S,\leq)$ an ordered monoid, $\omega:S \to End(R)$ a monoid homomorphism, and $A= R\left[\left[S,\omega \right]\right]$ the ring of skew generalized power series. The concepts of generalized Baer and…

In this article, we proceed on the transfer of the left endo-Noetherian property on certain ring extensions. We transfer of the right (left) endo-Noetherian property to the right (left) quotient rings. For a subring $T$ of $R$ and a finite…

A ring R shall be called F-noetherian if every finite subset of R is contained in a (left and right) noetherian subring of R . For example, every commutative ring is tightly F-noetherian in the sense that every finite subset of R generates…

In this paper, the notion of rings with uniformly S-w-Noetherian spectrum is introduced. Several characterizations of rings with uniformly S-w-Noetherian spectrum are given. Actually, we show that a ring R has uniformly S-w-Noetherian…

Birkenmeier and Heider, in [2], say that a ring R is right cP-Baer if the right annihilator of a cyclic projective right R-module in R is generated by an idempotent. These rings are a generalization of the right p.q.-Baer and abelian rings.…

In this note we consider the links of prime ideals of certain skew polynomial rings and prove our main theorem, namely theorem [5], which states the following.Let R be a noetherian ring that is link k-symmetric and let {\sigma} be an…

Let $R$ be a ring and $\sigma$ an endomorphism of $R$. In this note, we study skew polynomial rings and skew power series rings over idempotent reflexive rings and abelian rings. Also, we introduce the concept of right (resp., left)…

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 $R$ be a commutative ring with identity, $S\subseteq R$ be a multiplicative set and $J$ be an ideal of $R$. In this paper, we introduce the concept of $S$-$J$-Noetherian rings, which generalizes both $J$-Noetherian rings and…

The classical Noether Normalization Lemma states that if $S$ is a finitely generated algebra over a field $k$, then there exist elements $x_1,\dots,x_n$ which are algebraically independent over $k$ such that $S$ is a finite module over…

We study Noether's normalization lemma for finitely generated algebras over a division algebra. In its classical form, the lemma states that if $I$ is a proper ideal of the ring $R=F[t_1,\ldots,t_n]$ of polynomials over a field $F$, then…

In this paper, we introduce the concept of nonnil-S-Laskerian rings, which generalize both nonnil-Laskerian rings and S-Laskerian rings. A ring R is said to be nonnil-S-Laskerian if every nonnil ideal I (disjoint from S) of R is…

Let A be a semprime, right noetherian ring equipped with an automorphism alpha, and let B := A[[y; alpha]] denote the corresponding skew power series ring (which is also semiprime and right noetherian). We prove that the Goldie ranks of A…

In this paper, we investigate the structure of skew power series rings of the form $S = R[[x;\sigma,\delta]]$, where $R$ is a complete filtered ring and $(\sigma,\delta)$ is a skew derivation respecting the filtration. Our main focus is on…

The first purpose of this paper is to set up a general notion of skew power series rings S over a coefficient ring R, which are then studied by filtered ring techniques. The second subject consists of investigating the class of S-modules…