Let $A$ be a p-Banach algebra and $\alpha$ a two-sided ideal of $A$ with a complete
p-norm stronger than the p-norm inherited from $A$. By integral methods, we give here a holomorphic
functional calculus relatively to $\alpha$ which coïncides with the holomorphic functional
calculus defined in $A\vert\alpha$\, considered as a quotient quasi-Banach algebra. As application, we
get a version of Šilov's decomposition theorem. We also give the spectral mapping theorem and
an integral formula for the image of the k-th derivative of a holomorphic function.