On the investigations of Ivan Prodanov in the theory of abstract spectra

TL;DR

This paper provides detailed proofs and some new results on Ivan Prodanov's work concerning abstract spectra and separative algebras, which were previously announced but not fully published.

Contribution

It offers the first complete proof-based exposition of Prodanov's results and includes additional new findings in the theory of abstract spectra.

Findings

Complete proofs of Prodanov's results on abstract spectra

New results related to separative algebras

Clarification and extension of previous work

Abstract

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.