Trivial Extensions Defined by Coherent-like Conditions

By S. Kabbaj, Najib Mahdou. 2004

143 citations recorded by the source corpus.

Abstract This paper investigates coherent-like conditions and related properties that a trivial extension R ≔ A ∝ E might inherit from the ring A for some classes of modules E. It captures previous results dealing primarily with coherence, and also establishes satisfactory analogues of well-known coherence-like results on pullback constructions. Our results generate new families of examples of rings (with zerodivisors) subject to a given coherent-like condition.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b29c8e7e3de8a3939d60dee2853ff20f680376c2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Driss Bennis
2. S. Kabbaj
3. Najib Mahdou

In Geometry and Topology

1. Driss Bennis
2. Najib Mahdou

Citations in the corpus

• Rings Over Which the Class of Gorenstein Flat Modules is Closed Under Extensions (2008, background): “This means that there exist left GF-closed rings which are not right coherent (take for instance a non-semihereditary ring R with wdim( R  ≤ 1, see for example Kabbaj and Mahdou, 2004 , Example 2.”
• Trivial extensions defined by Prüfer conditions (2008, background): “The class of finite conductor rings properly contains the class of coherent (a fortiori, Noetherian and hence principal) rings [13,19].”