相关论文: Semistar invertibility on integral domains
In 1994, Matsuda and Okabe introduced the notion of semistar operation, extending the "classical" concept of star operation. In this paper, we introduce and study the notions of semistar linkedness and semistar flatness which are natural…
We introduce and study the notion of $\star$-stability with respect to a semistar operation $\star$ defined on a domain $R$; in particular we consider the case where $\star$ is the $w$-operation. This notion allows us to generalize and…
We give a classification of {\texttt{e.a.b.}} semistar (and star) operations by defining four different (successively smaller) distinguished classes. Then, using a standard notion of equivalence of semistar (and star) operations to…
In 1994, Matsuda and Okabe introduced the notion of semistar operation. This concept extends the classical concept of star operation (cf. for instance, Gilmer's book \cite{G}) and, hence, the related classical theory of ideal systems based…
Call a semistar operation $\ast$ on the polynomial domain $D[X]$ an extension (respectively, a strict extension) of a semistar operation $\star$ defined on an integral domain $D$, with quotient field $K$, if $E^\star = (E[X])^{\ast}\cap K$…
The purpose of this paper is to deepen the study of the Pr\"ufer $\star$--multiplication domains, where $\star$ is a semistar operation. For this reason, in Section 2, we introduce the $\star$--domains, as a natural extension of the…
Let $D$ be an integral domain and $\star$ a semistar operation stable and of finite type on it. In this paper we define the semistar dimension (inequality) formula and discover their relations with $\star$-universally catenarian domains and…
We provide a complete solution to the problem of extending arbitrary semistar operations of an integral domain $D$ to semistar operations of the polynomial ring $D[X]$. As an application, we show that one can reobtain the main results of…
Invertibility is an important concept in category theory. In higher category theory, it becomes less obvious what the correct notion of invertibility is, as extra coherence conditions can become necessary for invertible structures to have…
In this paper we study the star operations on a pullback of integral domains. In particular, we characterize the star operations of a domain arising from a pullback of ``a general type'' by introducing new techniques for ``projecting'' and…
Semi-invertible multiplicative ergodic theorems establish the existence of an Oseledets splitting for cocycles of non-invertible linear operators (such as transfer operators) over an invertible base. Using a constructive approach, we…
We prove a characterization of a P$\star$MD, when $\star$ is a semistar operation, in terms of polynomials (by using the classical characterization of Pr\"{u}fer domains, in terms of polynomials given by R. Gilmer and J. Hoffman…
We study the sets of semistar and star operation on a semilocal Pr\"ufer domain, with an emphasis on which properties of the domain are enough to determine them. In particular, we show that these sets depend chiefly on the properties of the…
The concepts of independence and totalness of subspaces are introduced in the context of quasi-probability distributions in phase space, for quantum systems with finite-dimensional Hilbert space. It is shown that due to the…
Let $D$ be a Pr\"ufer $\star$-multiplication domain, where $\star$ is a semistar operation on $D$. We show that certain ideal-theoretic properties related to idempotence and divisoriality hold in Pr\"ufer domains, and we use the associated…
The primary purpose of this paper is to investigate the question of invertibility of the sum of operators. The setting is bounded and unbounded linear operators. Some interesting examples and consequences are given. As an illustrative…
The concept of integral as an inverse to that of derivation was already introduced for rings and recently also for lattices. Since semirings generalize both rings and bounded distributive lattices, it is natural to investigate integration…
We show that the theory of quantales and quantic nuclei motivate new results on star operations, semistar operations, semiprime operations, ideal systems, and module systems, and conversely the latter theories motivate new results on…
This paper studies the notions of star and semistar operations over a polynomial ring. It aims at characterizing when every upper to zero in $R[X]$ is a $*$-maximal ideal and when a $*$-maximal ideal $Q$ of $R[X]$ is extended from $R$, that…
Let $R$ be a commutative integral domain and let $\star$ be a semistar operation of finite type on $R$, and $I$ be a quasi-$\star$-ideal of $R$. We show that, if every minimal prime ideal of $I$ is the radical of a $\star$-finite ideal,…