Topic
Overring
About: Overring is a research topic. Over the lifetime, 168 publications have been published within this topic receiving 2009 citations.
Papers published on a yearly basis
Papers
Posted Content•
TL;DR: In this paper, the authors introduce a new general construction, called the amalgamated duplication of a ring $R$ along an ideal module $E$ that they assume to be an ideal in some overring of $R$.
Abstract: We introduce a new general construction, denoted by $R\JoinE$, called the amalgamated duplication of a ring $R$ along an $R$--module $E$, that we assume to be an ideal in some overring of $R$. (Note that, when $E^2 =0$, $R\JoinE$ coincides with the Nagata's idealization $R\ltimes E$.)
After discussing the main properties of the amalgamated duplication $R\JoinE$ in relation with pullback--type constructions, we restrict our investigation to the study of $R\JoinE$ when $E$ is an ideal of $R$.
Special attention is devoted to the ideal-theoretic properties of $R\JoinE$ and to the topological structure of its prime spectrum.
144 citations
Book•
8 Aug 2015
TL;DR: In this article, Baer, Rickart, and Quasi-Baer rings were used to injectivity and some of its generalizations, including Matrix, Polynomial, and Group Ring Extensions.
Abstract: Preliminaries and Basic Results.- Injectivity and Some of Its Generalizations.- Baer, Rickart, and Quasi-Baer Rings.- Baer, Quasi-Baer Modules, and Their Applications.- Triangular Matrix Representations and Triangular Matrix Extensions.- Matrix, Polynomial, and Group Ring Extensions.- Essential Overring Extensions - Beyond the Maximal Ring of Quotients.- Ring and Module Hulls.- Hulls of Ring Extensions.- Applications to Rings of Quotients and C* Algebras.- Open Problems and Questions.- References.- Index.
109 citations
TL;DR: In this article, the authors extend the notion of ★-Noetherian domains to the semistar setting and show that a ★-Dedekind domain is an integral domain with the ascending chain condition on the set of its quasi-★-ideals.
64 citations
TL;DR: In this paper, the authors introduced the concept of conducive G-domains, which is an integral domain whose overrings, apart from the quotient field, have nonzero conductor.
63 citations
TL;DR: In this paper, it was shown that the w-integral closure of an integral domain is an integrally closed overring of the integral domain, and that it can be seen as an analog to the integral closure of strong Mori domains.
45 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 6 |
| 2020 | 6 |
| 2019 | 3 |
| 2018 | 7 |
| 2017 | 7 |
| 2016 | 8 |