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\title{\bf Implicative filters in finite lattice implication algebras  }
\maketitle

\begin{abstract}
 In this paper, by considering a finite lattice implication algebra L and A$\subset$L, the set of all co-atoms of L, we characterize the implicative filters of L.
 then we give conditions that a lattice implication algebras is H-implication.
 \end{abstract}
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\section{Preliminaries}
A map $f:(P, e_P )\rightarrow (Q, e_Q)$ between two $L$-ordered sets is called {\it monotone} if for all $x, y \in P$, $e_P(x,y)\leq e_Q(f(x), f(y))$. A monotone map $f:(P,e_P)\ra (Q,e_Q)$ is called an {\it $L$-isomorphism} if it is one to one and onto map.
\begin{defn}{\rm \cite{bdz}}
%Let $(P,e)$ be an $L$-ordered set and $S\in L^P$.
$S\in L^P$ is called {\it convex $L$-subset} of $L$-order set $(P,e)$, if for any $x,y,a\in P$,
\[S(x)\wedge S(y)\wedge e(x,a)\wedge e(a,y)\leq S(a)\]
\end{defn}
\bibliographystyle{remark}

\begin{thebibliography}{10}

\bibitem{Glass} 
A. M. W. Glass,  \emph{Partially Ordered Groups},  Word Scientific, (1999).

\bibitem{amc} M. Abad, C. R. Cimadamore, V. D�az, P. Jos�, \emph{Topological representation for monadic implication algebras}, Cent. Eur. J. Math. 7(2) (2009), 299-309.

\bibitem{bm75}
D. W. Borns and J. M. Mack, \emph{An Algebraic Introduction to Mathematical Logic}, Springer, Berlin, 1975.

\bibitem{bb94}
L. Bolc and P. Borowik, \emph{Many-valued Logic}, Springe, Berlin, 1994.

\bibitem{bs81}
S. Burris, H. P. Sankappanavar, \emph{A Corse in Universal Algebra}, Springer-Verlag, New York, 1981.

\bibitem{lx9l}
J. Liu and Y. Xu,  \emph{ On Certain Filters in Lattice Implication Algebras}, Chinese Quarterly J. Math, 11: 4 (1996), 106-111.

\bibitem{lx97}
J. Liu and Y. Xu,  \emph{ Filter and Structure of Lattice Implication Algebras}, Chinese Science Bulletin, 42: 18 (1997), 1517-1520.

\bibitem{x93}
Y. Xu,  \emph{ Lattice Implication Algebras}, J. Southwest Jiaotong Univ, 1 (1993), 20-27.
lx9l
\bibitem{Enf87}
Y. Xu and K. Y. Qin,  \emph{ Lattice H Implication Algebras and Lattice Implication Algebras Classes}, J. Hebei Mining and Civil Engineering Institute, 3 (1992), 139-143.

\bibitem{xq93}
Y. Xu and K. Y. Qin,  \emph{On Filters of Lattice Implication Algebras}, J. Fuzzy Math, 1:2 (1993), 251-260.

\bibitem{xrql03}
Y. Xu, D. Ruan, K. Y. Qin and J. Liu,  \emph{ Lattice-valued logic, An Alternative Approach to Treat Fuzziness and Incomparability}, Springer, Berlin, 2003.

\bibitem{yz} Y. Q. Zhu,  \emph{Finite simple lattice implication algebras}, Chinese Quarterly J. Math, 23(3) (2008), 423-429.

%\bibitem{cfl} R. A. Borzooei, S. F. Hosseiny, \emph{Characterization of %Finite Lattice Implication
%Algebras}
\end{thebibliography}


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