We first give general tools for working with cyclic cohomology of nondegenerate algebras. Using our way of approach in this paper, at least in general when we impose some extra conditions, one always has tomake sure that it is natural to look at the cyclic cohomology theory of algebras with an identity and to try to extend it to the algebras without identity but with a nondegenerate product. Thenwe associate a cyclic module structure to each regular multiplier Hopf algebra endowed with a modular pair in involution, as a motivating example.
