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\newcommand{\HRdim}{\mathop{\rm H\mbox{-}dim_R}\nolimits}
\newcommand{\CMdim}{\mathop{\rm CM\mbox{-}dim}\nolimits}
\newcommand{\Gdim}{\mathop{\rm G\mbox{-}dim}\nolimits}
\newcommand{\CIdim}{\mathop{\rm CI\mbox{-}dim}\nolimits}
\newcommand{\pd}{\mathop{\rm pd}\nolimits}

\begin{document}

\centerline{\large \bf Homological Dimensions}

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\centerline{Alexander A.~Gerko}
\centerline{\it Moscow State University, Russia}
\centerline{e-mail {\tt gerko@mccme.ru}}

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\par
%   Text of the abstract
In this talk we will define and describe some properties of {\rm CM}-dimension.
This invariant shares basic properties with projective dimension
(Auslander-Buchsbaum formula, good behavior under localization, etc.),
but provides a characterization for Cohen-Macaulay rings in a sense 
projective dimension does for regular rings. It also fits in a row

$$\pd_R M \geq \CIdim_R M \geq \Gdim_R M \geq \CMdim_R M,$$
where the middle terms are known, respectively, from works of Avramov,
Gasharov, Peeva and Auslander, Bridger. Also a number of questions on
{\it semi-dualizing complexes}
will be proposed, with partial results for {\it semi-dualizing} modules.

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