caa a22 4500 467882681 CHVBK 20180406152724.0 cr unu---uuuuu 170328e20061201xx s 000 0 eng 10.1007/s10485-006-9051-6 doi (NATIONALLICENCE)springer-10.1007/s10485-006-9051-6 Kadison Lars Department of Mathematics, David Rittenhouse Laboratory, 209 South 33rd Street, 19104-6395, Philadelphia, PA, USA aut Codepth Two and Related Topics [Elektronische Daten] [Lars Kadison] A depth two extension A | B is shown to be weak depth two over its double centralizer V A (V A (B)) if this is separable over B. We consider various examples and non-examples of depth one and two properties. Depth two and its relationship to direct and tensor product of algebras as well as cup product of relative Hochschild cochains is examined. Section6 introduces a notion of codepth two coalgebra homomorphism g : C → D, dual to a depth two algebra homomorphism. It is shown that the endomorphism ring of bicomodule endomorphisms End D C D forms a right bialgebroid over the centralizer subalgebra g * : D * → C * of the dual algebra C *. Springer Science + Business Media B.V., 2006 Hochschild cochains nationallicence codepth two nationallicence bicomodule endomorphisms nationallicence Applied Categorical Structures Kluwer Academic Publishers 14/5-6(2006-12-01), 605-625 0927-2852 14:5-6<605 2006 14 10485 https://doi.org/10.1007/s10485-006-9051-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10485-006-9051-6 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kadison Lars Department of Mathematics, David Rittenhouse Laboratory, 209 South 33rd Street, 19104-6395, Philadelphia, PA, USA aut NATIONALLICENCE 773 0- Applied Categorical Structures Kluwer Academic Publishers 14/5-6(2006-12-01), 605-625 0927-2852 14:5-6<605 2006 14 10485 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer