Ytdyklly

Those days I write a book, and I use framed boxes tcolorbox. Have a look:

documentclass[12pt,a4paper]{book}

usepackage[utf8]{inputenc}

usepackage{amsmath,amsthm,amsfonts,amssymb,mathtools}

usepackage[english]{babel}

usepackage{graphicx}

usepackage{textcomp}

usepackage{tcolorbox,xcolor}

theoremstyle{definition}



makeatletter



tcbuselibrary{theorems}



newtcbtheorem[number within=section]{mytheo}{Theorem}%

{colback=black!5,colframe=red!35!black,fonttitle=bfseries}{th}



newtcbtheorem[number within=section]{myprop}{Proposition}%

{colback=black!5,colframe=red!50!black,fonttitle=bfseries}{th}



newtcbtheorem[number within=section]{mylem}{Lemma}%

{colback=black!5,colframe=red!50!black,fonttitle=bfseries}{th}



newtcbtheorem[number within=section]{mypor}{Corollary}%

{colback=black!5,colframe=red!35!black,fonttitle=bfseries}{th}



newtcbtheorem[number within=section]{myax}{Axiom}%

{colback=black!5,colframe=blue!35!black,fonttitle=bfseries}{th}





renewcommand{rmdefault}{udidot}



begin{document}



newtheorem{defin}{Definition}[section]

newtheorem{prt}{Remark}[section]

newtheorem{prts}{Remarks}[section]

newtheorem{exmp}{Example}[section]

newtheorem{exmps}{Examples}[section]

newtheorem*{note}{Note}



chapter{Maximal and Prime Ideals}



section{Maximal Ideals}  



begin{defin}  

Let $R$ a commutative ring with $1_R$ ...

end{defin}



begin{myprop}{Maximal Ideals Criterion}{}

    label{Max Id Crit}

Let $R$ a commutative ring with $1_R$ ...

end{myprop}



From the Proposition ref{Max Id Crit}, ...



end{document}

As you can see, I would like to use these frames only for theorems, propositions, lemmas, corollaries and axioms (and not for the definitions). Also I would like to keep the choice to write some of them (for instance, a theorem) without these frames.

My questions are:

1. How can we have consecutive numbering in the whole text?


2. Ase you can see, we face a problem with labels in the reference of theorems etc. How can we solve it?

1. The tcbtheorem environments allow you to use counters from other tcbtheorems as well as existing LaTeX counters. It will be easier to define the standard LaTeX theorems first (all sharing the same counter), and then define the tcbtheorems (using that same counter).


2. The problem is that a label for a tcbtheorem environment needs to be passed as an option to that environment in order for it to work correctly. This is not standard LaTeX behaviour (you would have noticed that labelling and referencing your definition environment would have worked without a hitch).

documentclass[12pt,a4paper]{book}

usepackage[utf8]{inputenc}

usepackage{amsmath,amsthm,amsfonts,amssymb,mathtools}

usepackage[english]{babel}

usepackage{graphicx}

usepackage{textcomp}

usepackage{tcolorbox,xcolor}

theoremstyle{definition}

% Define amsthm theorems first

newtheorem{defin}{Definition}[section] % Creates a new counter, number within section

newtheorem{prt}[defin]{Remark} % Putting [defin] in second position uses defin's counter instead of creating a new one

newtheorem{prts}[defin]{Remarks} % Again share defin's counter

newtheorem{exmp}[defin]{Example} % etc.

newtheorem{exmps}[defin]{Examples}

newtheorem*{note}{Note}



tcbuselibrary{theorems}

% use counter*=defin to make each tcbtheorem share defin's counter

newtcbtheorem[use counter*=defin, number within=section]{mytheo}{Theorem}%

{colback=black!5,colframe=red!35!black,fonttitle=bfseries}{th}

newtcbtheorem[use counter*=defin, number within=section]{myprop}{Proposition}%

{colback=black!5,colframe=red!50!black,fonttitle=bfseries}{th}

newtcbtheorem[use counter*=defin, number within=section]{mylem}{Lemma}%

{colback=black!5,colframe=red!50!black,fonttitle=bfseries}{th}

newtcbtheorem[use counter*=defin, number within=section]{mypor}{Corollary}%

{colback=black!5,colframe=red!35!black,fonttitle=bfseries}{th}

newtcbtheorem[use counter*=defin, number within=section]{myax}{Axiom}%

{colback=black!5,colframe=blue!35!black,fonttitle=bfseries}{th}

renewcommand{rmdefault}{udidot}

begin{document}

chapter{Maximal and Prime Ideals}

section{Maximal Ideals}  

% Normal labelling

begin{defin}  label{first_def}

Let $R$ a commutative ring with $1_R$ ...

end{defin}

% tcbtheorem labelling

begin{myprop}[label=prop:maximal]{Maximal Ideals Criterion}{}

Let $R$ a commutative ring with $1_R$ ...

end{myprop}

From the Proposition ref{prop:maximal} and definition ref{first_def}ldots

end{document}

Output:

As an aside, I would recommend using the cleveref package which can easily be set-up with the each tcbtheorem so as to produce a named reference instead of just a number e.g. 'proposition 1.1.2' vs '1.1.2'. That way you don't have to worry about whether you're referencing a theorem, or a definition, or a proposition etc. each time.

FYI There was a rogue makeatletter in your code.

The key is the tcolorbox options use counter=<another counter> and use counter from= <counter from another tcolorbox>

Update taking into account the OP comments:

documentclass[12pt,a4paper]{book}

usepackage[utf8]{inputenc}

usepackage{amsmath,amsthm,amsfonts,amssymb,mathtools}

usepackage[english]{babel}

usepackage{graphicx}

usepackage{textcomp}

usepackage{tcolorbox,xcolor}

theoremstyle{definition}



%makeatletter



tcbuselibrary{theorems}



newtcbtheorem[number within=section,use counter=defin]{mytheo}{Theorem}%

{colback=black!5,colframe=red!35!black,fonttitle=bfseries}{th}



newtcbtheorem[number within=section,use counter =defin]{myprop}{Proposition}%

{colback=black!5,colframe=red!50!black,fonttitle=bfseries}{th}



newtcbtheorem[number within=section,use counter= defin]{mylem}{Lemma}%

{colback=black!5,colframe=red!50!black,fonttitle=bfseries}{th}



newtcbtheorem[number within=section,use counter=defin]{mycor}{Corollary}%

{colback=black!5,colframe=red!35!black,fonttitle=bfseries}{th}



newtcbtheorem[number within=section,use counter=defin]{myax}{Axiom}%

{colback=black!5,colframe=blue!35!black,fonttitle=bfseries}{th}





renewcommand{rmdefault}{udidot}



begin{document}



newtheorem{defin}{Definition}[section]

newtheorem{prt}[defin]{Remark}

newtheorem{prts}[defin]{Remarks}

newtheorem{exmp}[defin]{Example}%[section]

newtheorem{exmps}[defin]{Examples}

newtheorem*{note}{Note}



chapter{Maximal and Prime Ideals}



section{Maximal Ideals}  



begin{defin} 

label{def:commutative ring}

Let $R$ a commutative ring with $1_R$ ...

end{defin}



begin{myprop}{Maximal Ideals Criterion}{Max Id Crit}



Let $R$ a commutative ring with $1_R$ ...

end{myprop}



From the Proposition ref{th:Max Id Crit}, 



See definition ref{def:commutative ring}



begin{exmp} label{ex: my example}

my example

end{exmp}



example : ref{ex: my example}







end{document}