\titleofpresentation{Application of  polytope method to   irreducibility of
  polynomials  over $\mathbb{Z}_{p^k}$}

\presenter{Fatih Koyuncu}  %  Name just one speaker, please; collaborators
			%  can be credited in the body of the abstract.

Ostrowski observed that there is a relation between    the factorization   of a
polynomial $f\in F[x_1,\dots ,x_n]$ for  any field $F$ and   the integral decomposition,
with respect
to Minkowski sum,  of the Newton polytope
of $f$. Here,  extending   this result  to   some families of polynomials
in   $R[x_1,\dots ,x_n]$ for an arbitrary  ring  $R$,  we have found infinitely many
classes of  multivariate  polynomials which are irreducible over
 $\mathbb{Z}_n$ for any  positive integer $n$,
in particular,
over  $\mathbb{Z}_{p_i^k}$ for any   prime number $p_i$ and
arbitrary positive integer  $k$.
%  [Body of abstract goes here.]



\begin{ourbiblio}{199}
\bibitem [1] {koyuncu(1)}  Gao S.  \textsl{Absolute irreducibility of polynomials  via
Newton polytopes}, Journal of Algebra \textbf{237} (2001), No.2 501-520.
\bibitem [2]  {koyuncu(2)} Ostrowski  A.M.  \textsl{ On multiplication and factorization
of polynomials,  I.  Lexicographic orderings and extreme aggregates of terms},
Aequationes Math. \textbf{13} (1975), 201-228.

\end{ourbiblio}


\presenteraddress{Fatih Koyuncu} 

\textit{Mu\u gla University, Department of Mathematics}

\email{fatih@mu.edu.tr}



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