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The Frobenius depth denoted by $\Fdepth$ defined by Hartshorne-Speiser in1977 and later by Lyubeznik in 2006, in a different way, for rings of positivecharacteristic. The aim of the present paper is to compare the $\Fdepth$ withformal grade, and $\depth$ to shed more light on the notion of Frobenius depthfrom a different point of view.

On cohomological invariants of local rings in positive characteristic