  Starting from a very general trace-form entropy, we introduce a pair of
algebraic structures endowed by a generalized sum and a generalized product.
These algebras form, respectively, two Abelian fields in the realm of the
complex numbers isomorphic each other. We specify our results to several
entropic forms related to distributions recurrently observed in social,
economical, biological and physical systems including the stretched
exponential, the power-law and the interpolating Bosons-Fermions distributions.
Some potential applications in the study of complex systems are advanced.
