Depth of noncommutative subrings

<p>In <a href="/facts/Ring_theory/VW6svEFe">ring theory</a> and <a href="/facts/Frobenius_algebra/xnxIFzQ7">Frobenius algebra</a> extensions, areas of <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, there is a notion of depth two  subring or depth of a Frobenius extension.  The notion of depth two is important in a certain  noncommutative Galois theory, which generates <a href="/facts/Hopf_algebroid/56k17Ea1">Hopf algebroids</a> in place of the more classical <a href="/facts/Galois_group/A0p35p5c">Galois groups</a>, whereas the notion of depth greater than two measures the defect, or distance, from being depth two in a tower of iterated <a href="/facts/Endomorphism_ring/K1UgpnJK">endomorphism rings</a> above the <a href="/facts/Subring/M0perybt">subring</a>. A more recent definition of depth of any unital subring in any associative ring is proposed (see below) in a paper studying the depth of a <a href="/facts/Subgroup/r91mBgpa">subgroup</a> of a <a href="/facts/Finite_group/vv2tvogB">finite group</a> as <a href="/facts/Group_ring/TJlkt5Te">group algebras</a> over a <a href="/facts/Commutative_ring/QS1r2ovR">commutative ring</a>.
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Depth of noncommutative subrings open-in-new

Depth of noncommutative subrings