Zero-product (Jordan zero-product) preserving maps on certain algebras

We introduce the notion of strongly zero-product (strongly Jordan zero-product) preserving maps on normed algebra. Also for the non-zero vector space V and for the non-zero linear functional f on V, we equip V with a multiplication, converting V into an associative algebra, denoted by Vf . We char- acterize the zero-product(Jordan zero-product)preserving maps on Vf . Also we characterize the strongly zero-product(strongly Jordan zero-product)preserving maps on Vf in the case where V is a normed vector space and f is a continuous linear functional on V. Finally, some illustrating examples are given.