Artinian rings which are not generalized Rickart
Ali Shahidikia
TL;DR
This paper demonstrates that certain non-unital right artinian rings do not possess the generalized Rickart property, providing specific examples to challenge previous assumptions in ring theory.
Contribution
It introduces examples of non-unital right artinian rings that are not generalized Rickart, disproving a prior corollary for this class of rings.
Findings
Existence of non-unital right artinian rings that are not generalized Rickart
Counterexamples to previous corollaries in ring theory
Clarification of properties of non-unital artinian rings
Abstract
In this note, we show that there exist non-unital right artinian rings which are not generalized Rickart. In particular, we provide examples to show that, [16, Corollary 2.31] is not true for non-unital artinian rings.
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Taxonomy
TopicsCancer Mechanisms and Therapy · Rings, Modules, and Algebras