On bilinear maps through zero products

‎In this article we study the bilinear maps of algebras which are zero on elements with zero products and we present the notion of zero product determined algebra‎. ‎Then we review some results about this notion‎. ‎More precisely‎, ‎first we study the properties of zero product determined algebras‎, ‎then we will give some algebras which are non-zero product determined or zero product determined algebras‎, ‎especially we will examine whether some nest algebras on a‎ ‎Banach or Hilbert space is zero product determined‎. ‎Also we introduce some related open problems‎.