Published January 1, 2022
| Version v1
Journal article
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On the extent of the injectivity of direct sums of modules
Creators
- 1. Ohio Univ, Dept Math, Athens, OH 45701 USA
- 2. Hacettepe Univ, Dept Math, TR-06800 Ankara, Turkey
Description
Inspired by the fact that a ring is right Noetherian if and only if direct sums of certain injective right modules are once again injective, we propose a way to not only decide whether a ring is Noetherian but to gauge how Noetherian an arbitrary ring is. As an application of this line of thinking, volatile rings, a notion opposite to Noetherianness, are introduced. Characterizations for right volatile rings, meant as counterparts to corresponding characterizations of right Noetherian rings, are given. Examples of volatile rings as well as of rings that are neither Noetherian nor volatile are presented.
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