  In this paper, we define generalized splitting and element splitting
operations on $p$-matroids. $p$-matroids are the matroids representable over
$GF(p).$ The circuits and the bases of the new matroid are characterized in
terms of circuits and bases of the original matroid, respectively. A class of
$n$-connected $p$-matroids which gives n-connected $p$- matroids using the
generalized splitting operation is also characterized. We also prove that
connectivity of $p$-matroid is preserved under element splitting operation.
Sufficient conditions to obtain Eulerian $p$-matroid from Eulerian $p$-matroid
under splitting and element splitting operations are provided.
