# Preparing an abstract

## How to prepare an abstract?

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### The format of the abstract

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We ask all of you who want to submit an abstract for the conference to prepare it using LaTeX2e (LaTeX) and in the following format:

       \begin{myabstract}

\begin{start}
{Speaker}
{Title of the talk}
...\\
\end{start}

The abstract text

\begin{references}{The widest reference}
\item[Name of reference 1] Reference number 1
\item[Name of reference 2] Reference number 2
.
.
.
\item[Name of last reference] Last reference
\end{references}

\coauthor{Name of first coauthor}
...\\
\coauthor{Name of second coauthor}
...\\

.
.
.

\coauthor{Name of last coauthor}
...\\

\end{myabstract}


### Predefined commands

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We plan to compile the abstracts in one LaTeX document, so we need to have some standards when it comes to defining user defined commands. We supply a list below of commands that most probably will cover most of your needs, but if you do not find the command that you need on this list, put your definitions after

\begin{myabstract}
and before
\begin{start}
%
% Functors, Hom, End, Ext, ....
%
\Hom   ----> Hom
\uHom  ----> underlined Hom
\oHom  ----> overlined Hom
\End   ----> End
\uEnd  ----> underlined End
\oEnd  ----> overlined End
\Irr   ----> Irr
\Aut   ----> Aut
\soc   ----> soc
\ann   ----> ann
\Tor   ----> Tor
\Ext   ----> Ext
\Tr    ----> Tr, the transpose
%
% Categories, subcategories
%
\mod   ----> mod
\Mod   ----> Mod
\ind   ----> ind
\umod  ----> underlined mod
\omod  ----> overline mod
\Morph ----> Morph
\Sub   ----> Sub
\Fac   ----> Fac
\Supp  ----> Supp
\Ab    ----> Ab
\Rep   ----> Rep
%
% Objects, kernel, cokernel, images, etc.
%
\Im    ----> Im
\Ker   ----> Ker
\Coker ----> Coker
\Spec  ----> Spec
\Gl    ----> Gl
\Sl    ----> Sl
%
% Dimensions, rank, etc.
%
\pd     ----> pd, projective dimension
\id     ----> id, injective dimension
\domdim ----> dom.dim, dominant dimension
\rank   ----> rank
\depth  ----> depth
\length ----> script l for length
\dim    ----> dim
\udim   ----> underlined dim
\findim ----> fin.dim, finitistic dimension
\gldim  ----> gl.dim, global dimension
\kar    ----> char
%
% Ideals
\m   ----> underline roman lower care m
\r   ----> underlined roman lower case r
%
% Misecellaneous
%
\op     ----> op, opposite
\c{ }   ----> \c{A}, gives caligraphic A, ....
\bbb{ } ----> blackboard bold characters, \bbb{C} gives complex numbers
\Sets   ----> Sets


### Theorems and other stuff

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To typeset a theorem use the following format:

         \begin{theorem}
Let $\Lambda$ be an artin algebra and $M$ an indecomposable
module in $\mod\Lambda$. Then $\End_\Lambda(M)$ is a local
ring.
\end{theorem}


If you want to put an attribute to the theorem, you do the following

         \begin{theorem}[Auslander]


This will come out like

Theorem 1 (Auslander)

if for example this is the first result mentioned in the abstract.

To typeset a corollary, conjecture, lemma, proposition or definition, just substitute theorem with the wanted word, namely, write exactly corollary, conjecture, lemma, proposition or definition instead of theorem.

Theorems, corollaries, lemmas, propositions and definitions will be numbered with the same counter, while conjectures will be numbered by their own counter.

### List of references

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Suppose we have the following 4 references

• M. Auslander, Coherent Functors, Proc. Conf. Categorical Algebra (Springer, New York, 1966).
• M. Auslander and I. Reiten, Representation theory of artin algebras III: Almost split sequences, Comm. in Algebra 3 (1975) 239-294.
• M. Auslander, I. Reiten and Sverre O. Smalø, Representation theory for artin algebras, Cambridge University Press, Cambridge studies in advanced mathematics, 36.
• M. Auslander and S. Sverre O. Smalø, Almost split sequences in subcategories, J. Algebra 69 (2) (1981) 426-454.
We want to label the references A, AR, ARS and AS. The widest reference is then ARS. To typeset using our reference environment it would look as follows
       \begin{references}{ARS}
\item[A] M.\ Auslander, {\em Coherent Functors}, Proc.\
Conf.\ Categorical Algebra (Springer, New York, 1966).
%
\item[AR] M.\ Auslander and I.\ Reiten, {\em Representation
theory of artin algebras III: Almost split sequences},
Comm.\ in Algebra 3 (1975) 239--294.
%
\item[ARS] M.\ Auslander, I.\ Reiten and Sverre O.\ Smal\o,
{\em Representation theory for artin algebras}, Cambridge
University Press, Cambridge studies in advanced mathematics, 36.
%
\item[AS] M.\ Auslander and S.\ Sverre O. Smal\o, {\em Almost
split sequences in subcategories}, J.\ Algebra 69 (2) (1981)
426--454.
\end{references}


### A complete example

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\documentclass{report}                    % If you have LaTeX2e, leave it
\usepackage{abstract2e}                   % as it is.
%\documentstyle[abstractplain]{report}    % If you have LaTeX, uncomment
% this line and comment out the
\begin{document}                          % two first lines with %-sign.

\begin{myabstract}
\begin{start}
{\O yvind Solberg}
{How, why and where for abstracts}
{solberg@matstat.unit.no}
Institutt for matematikk og statistikk\\
Norges teknisk-naturvitenskapelige universitet\\
N--7055 Dragvoll\\
Norway
\end{start}

This talk deals with the very difficult problem: {\em How to give a
talk using all the predefined commands that we have given?} Well, that
is really difficult, so we give up right away.

First we give examples of how to use the predefined commands:

$\Hom_\Lambda(A,B)$, $\uHom_\Lambda(A,B)$, $\oHom_\Lambda(A,B)$,
$\End_\Lambda(A)$, $\uEnd_\Lambda(A)$, $\oEnd_\Lambda(A)$, $\Irr(A,B)$,
$\Aut(\Gamma)$, $\Coker(f)$, $\rad^n(A,B)$, $\soc(M)$, $\ann_\Lambda(X)$,
$\Tor^\Lambda_i(A,B)$, $\Ext_\Lambda^i(A,B)$, $\Tr(M)$\bigskip

$\mod\Lambda$, $\Mod R$, $\ind\Lambda$, $\umod\Lambda$,
$\omod\Lambda$, $\Morph(\c{P}(\Lambda))$, $\Sub(M)$, $\Fac(M)$, $\Supp F$,
$\Ab$, $\add X$, $\Rep(\alpha)$\bigskip

$\Im f$, $\Ker f$, $\Coker f$, $\Spec(A)$, $\Gl_n(K)$, $\Sl_n(K)$\bigskip

$\pd_\Lambda(X)$, $\id_\Lambda(X)$, $\domdim\Lambda$, $\rank(F)$, $\depth(R)$,
$\length(X)$, $\dim(X)$, $\udim(X)$, $\findim(\Lambda)$, $\gldim(\Lambda)$,
$\kar k$\bigskip

$\m$, $\r$\bigskip

$\Lambda^\op$, $\c{A}$, $\c{B}$, $\Sets$, $\bbb{A}$, $\bbb{Z}$,
$\bbb{Q}$\bigskip

We are now ready to state the first theorem.

\begin{theorem}[Auslander]
Let $\Lambda$ be a semiprimary algebra over a field $K$. Let
$N$ be the radical of $\Lambda$ and $\Gamma=\Lambda/N$. If
$$\dim\Lambda<\infty \textrm{\ and\ } (\Gamma\colon K)<\infty,$$
then $$\dim\Lambda=\gldim\Lambda.$$
\end{theorem}
This theorem appeared in [A]. Another result that was proved there is
the following proposition.

\begin{proposition}
Let $\Lambda$ and $\Sigma$ be rings and $\varphi\colon \Lambda\to \Sigma$
a ring epimorphism. If $\Lambda$ is a semiprimary ring with radical $N$,
then $\Sigma$ is a semiprimary ring with radical $\varphi(N)$.
\end{proposition}

The following conjecture is mentioned in [ARS] on page 410.
\begin{conjecture}
Let $\Lambda$ be an artin algebra and $S$ a simple $\Lambda$-module. Then
$\Ext_\Lambda^i(S,\Lambda)\neq (0)$ for some $i$.
\end{conjecture}

\begin{references}{ARS}
\item[A] M.\ Auslander, On the dimension of modules and algebras, VI;
{\em Comparison of global and algebra dimension}, Nagoya Mathematical
Journal, vol.\ 11 (1957) 61--65.
%
\item[AR] M.\ Auslander and I.\ Reiten, {\em Representation
theory of artin algebras III: Almost split sequences},
Comm.\ in Algebra 3 (1975) 239--294.
%
\item[ARS] M.\ Auslander, I.\ Reiten and Sverre O.\ Smal\o,
{\em Representation theory for artin algebras}, Cambridge
University Press, Cambridge studies in advanced mathematics, 36.
\end{references}
%
\coauthor{Idun Reiten}{idun.reiten@avh.unit.no}
{Institutt for matematikk og statistikk\\
Norges teknisk-natur\-viten\-skape\-lige universitet\\
N-7055 Dragvoll\\
Norway}
%
\coauthor{Sverre O.\ Smal\o}{sverre.smalo@avh.unit.no}
{Institutt for matematikk og statistikk\\
Norges teknisk-natur\-viten\-skape\-lige universitet\\
N-7055 Dragvoll\\
Norway}
%
\end{myabstract}
%
\end{document}


### Style file, example file and instruction file

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We have prepared the style file both in LaTeX2e and old LaTeX format. If you do not know the difference between these, you can use the style file for LaTeX, which hopefully should work independent of what version of LaTeX you are using. To test your typesetting you need a copy of one of the style files, and the example file shows how you can test your typesetting using LaTeX or LaTeX2e.

Using Netscape, clicking on one of the following options you will get a new window labeled Save As or get the file displayed on the screen. If you get a new window, choose on which directory you want to save the file, and then, click on OK to save; if you get the file displayed on the screen, choose Save As under the label File in the menu bar.

Using Mosaic, clicking on one of the following options you will get the file displayed on the screen. Under File on the menu bar choose Save as ... and then you will get new window labeled Save Document. Choose on which directory you want to save the file, and then enter the file name and click on OK to save.

If you are using another system or have problems, ask your local expert.

## JUNE 15-th 1996

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ICRA VIII <icra@matstat.unit.no>