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% $Id: SemiRng.tex,v 1.1.1.3 2004/10/04 17:25:13 nthiery Exp $
% File:		lib/DOMAINS/CATEGORY/DOC/SemiRng.tex
% Authors:	Nicolas M. Thiéry <nthiery@users.sourceforge.net>
% Purpose:	Documentation for the category Cat::SemiRng
% Created:	Wed Sep  3 14:52:42 2003
% License:	LGPL
% Project:	MuPAD-Combinat, http://mupad-combinat.sf.net
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\begin{Mhelppage}{SemiRng}{Nicolas M. Thiéry}
  [ImplState=stable,TestState=stable,DocState=stable]
%\Mproofread{...}{...}{...}

\begin{MInfo}
  \eng{the category of semi-rings without unit}
  \de{}
\end{MInfo}

\Mproofread{nthiery}{22/09/2003}{complete, but not proofread}

\begin{MIntro}
  \eng{\Mthis{} represents the category of semi-rings without unit.}
  \de{}
\end{MIntro}

\begin{MCatConst}
  \MCall{}
\end{MCatConst}

\begin{MCategories}
  \Mup{Cat::AbelianMonoid},
  \Mup{Cat::Monoid},
\end{MCategories}

\begin{MDetails}
  \eng{A \Mthis{} is essentially a ring without unit (\Mup{Cat::Rng}),
    except that the operation \Mup{+} (\Mup{_plus}) is not required to
    be invertible.  In other words, this is an abelian monoid
    according to the operation \Mex{+} and a non-abelian semi-group
    according to the operation \Mex{*} (\Mup{_mult}) where in addition
    the two distributive laws $a (b + c) = a b + a c$ and $(a + b) c =
    a c + b c$ hold.}

  \de{}
\end{MDetails}

%\begin{MDomBasEntries}
%  \MDomEntry{bla}
%  \eng{.}
%  \de{}
%\end{MDomBasEntries}

\begin{MChanges}
  \version{3.0}
  \eng[New category]{\Mthis{} is a new category} %
\end{MChanges}

\end{Mhelppage}
