  The results of Iv. Prodanov on abstract spectra and separative algebras were
announced in the journal "Trudy Mat. Inst. Steklova", 154, 1983, 200--208, but
their proofs were never written by him in the form of a manuscript, preprint or
paper. Since the untimely death of Ivan Prodanov withheld him from preparing
the full version of this paper and since, in our opinion, it contains
interesting and important results, we undertook the task of writing a full
version of it and thus making the results from it known to the mathematical
community. So, the aim of this paper is to supply with proofs the results of
Ivan Prodanov announced in the cited above paper, but we added also a small
amount of new results. The full responsibility for the correctness of the
proofs of the assertions presented below in this work is taken by us; just for
this reason our names appear as authors of the present paper.

General Topology;Category Theory;Rings and Algebras