  Let $A$ be an algebra in a monoidal category $\Cc$, and let $X$ be an object
in $\Cc$. We study $A$-(co)ring structures on the left $A$-module $A\ot X$.
These correspond to (co)algebra structures in $EM(\Cc)(A)$, the Eilenberg-Moore
category associated to $\Cc$ and $A$. The ring structures are in bijective
correspondence to wreaths in $\Cc$, and their category of representations is
the category of representations over the induced wreath product. The coring
structures are in bijective correspondence to cowreaths in $\Cc$, and their
category of corepresentations is the category of generalized entwined modules.
We present several examples coming from (co)actions of Hopf algebras and their
generalizations. Various notions of smash products that have appeared in the
literature appear as special cases of our construction.
