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Given a pair of non-commutative rings $(R, S)$, how to construct a faithfully semidualizing $(R, S)$-bimodule?

Henrik Holm and Diana White introduced the concept of faithfully semidualizing bimodules in the paper named "Foxby equivalence over associative rings".

Semidualizing modules provide a generalization of a free module of rank one, that is, any ring $R$ with a unit is a semidualizing module. Semidualizing modules are also called generalized tilting modules (see Wakamatsu, Tilting modules and Auslander's Gorenstein property, Corollary 3.2). These modules share some of the basic properties with their subclass consisting of all tilting modules. It is still an open problem - known as the Wakamatsu Tilting Conjecture - whether any Wakamatsu tilting module of finite projective dimension is tilting. Since faithfully semidualizing bimodules have more nice properties, we hope to find more examples.

For more details, see Holm, White, Foxby equivalence over associative rings.

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    $\begingroup$ You are much more likely to get an answer to your question if you provide a little more background. What is a semidualizing bimodule? What does the paper say? $\endgroup$
    – MTS
    Feb 22, 2012 at 2:58
  • $\begingroup$ semidualizing bimodules are also called Wakamatsu tilting modules or generalized tilting modules. $\endgroup$
    – Aimin Xu
    Apr 29, 2012 at 1:36

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