Title of paper covering odd numbers on right top of page?

If you want to submit this article to a journal, I strongly suggest to not change the layout. Think very hard if you really cannot provide a short version of the title for the headline, e.g.

\title[Brown-McCoy Radical \& properties in B-topological Rings]{Brown-McCoy Radical and its properties in B-topological Rings}

If you don't plan to submit this to a journal, you have more possibilities.

• use another documentclass

• use a smaller font size, e.g.

  \documentclass[a4paper,11pt,reqno, twoside]{amsart}
  

• enlarge the text width with

  \usepackage{geometry}
  

• don't use uppercaseing for the header

    \documentclass[a4paper,12pt,reqno, twoside]{amsart}
    \usepackage{amsmath}
    \usepackage{amsfonts}
    \usepackage{amssymb}
    \usepackage{amsthm}
    \usepackage{color}
    \usepackage{ifpdf}
    \usepackage{array}
    
    \usepackage{url}
    \usepackage{graphicx}
    \usepackage{float}
    \usepackage{multirow,bigdelim}
    
    \usepackage{hyperref}% http://ctan.org/pkg/hyperref
    \usepackage{cleveref}% http://ctan.org/pkg/cleveref
    \usepackage{lipsum}% http://ctan.org/pkg/lipsum
    \usepackage{chngcntr}% http://ctan.org/pkg/lipsum
    
    \usepackage{epstopdf} 
    \def\numset#1{{\\mathbb #1}}
    
    
    
    %\makeatletter
    %\let\std@footnotetext\@footnotetext
    %\usepackage{setspace}
    %\let\@footnotetext\std@footnotetext
    %\makeatother
    
    %\usepackage[margin=4.0cm]{geometry}
    
    
    \theoremstyle{plain}
    \newtheorem{Th}{Theorem}[section]
    \newtheorem{Lemma}[Th]{Lemma}
    \newtheorem{Cor}[Th]{Corollary}
    \newtheorem{Prop}[Th]{Proposition}
    
    \theoremstyle{definition}
    \newtheorem{Def}[Th]{Definition}
    \newtheorem{Conj}[Th]{Conjecture}
    \newtheorem{Rem}[Th]{Remark}
    \newtheorem{?}[Th]{Problem}
    \newtheorem{Ex}[Th]{Example}
    
    \newcommand{\im}{\operatorname{im}}
    \newcommand{\Hom}{{\rm{Hom}}}
    \newcommand{\diam}{{\rm{diam}}}
    \newcommand{\ovl}{\overline}
    %\newcommand{\M}{\mathbb{M}}
    
    \newcommand\blfootnote[1]{%
      \begingroup
      \renewcommand\thefootnote{}\footnote{#1}%
      \addtocounter{footnote}{-1}%
      \endgroup
    }
    

    \begin{document}

\title{Brown-McCoy Radical and its properties in B-topological Rings}
\author{Bhaskar Vashishth}
\author{Davinder Singh}


\address{University of Delhi \\ Department of Mathematics \\ 110 007}
\email{a.com}
\address{Sri  \\ University of Delhi \\ 110 017}
\email{ds.com}



\begin{abstract} The 
\end{abstract}

\keywords{$B$-topological ring }



\subjclass[2010]{Primary 54H13; Secondary 54D20.}
\maketitle

\markboth{Bhaskar Vashishth and Davinder Singh}{Brown-McCoy Radical and its properties in B-topological Rings}

\section{Introduction} 
\lipsum
\lipsum


\end{document}