Some results on local homology and local cohomology modules (Q2509811)

Let \(R\) be a commutative Noetherian local ring. The paper studies a theory of local homology modules which is dual to Grothendieck's theory of local cohomology modules which was defined by \textit{J. P. C. Greenlees} and \textit{J. P. May} [J. Algebra 149, No. 2, 438--453 (1992; Zbl 0774.18007)] and studied further by \textit{N. T. Cuong} and \textit{T. T. Nam} [J. Algebra 319, No. 11, 4712--4737 (2008; Zbl 1143.13021)]. Let \(R\) be a Noetherian local ring and \(\mathfrak{a}\) be an ideal of \(R\). In the paper under review, the author shows that for any Artinian \(R\)-module \(M\) the following equality holds: \[ \inf\{i\in\mathbb{N}: H^{\mathfrak{a}}_i(M)\,\,\, \text{is not representable}\}= \inf\{i\in\mathbb{N}:\mathfrak{a}\nsubseteq\sqrt{(0:H^{\mathfrak{a}}_i(M))}\}. \]