Gelfand-Mazur theorems in normed algebras: a survey (Q1639660)

The paper is a survey of results generalizing the well-known Gelfand-Mazur theorem, mainly for the class of Banach algebras. No proofs are presented. The discussion gives some good hints about most of the proofs and all results are clearly supplied with the references, where the interested reader can find the proofs. Although in the Section~8(e), some words are said about more general (non-normed, not locally convex) topological algebras, references to the works of \textit{M. Abel} [Uch. Zap. Tartu. Gos. Univ. 899, 65--70 (1990; Zbl 0762.46038); Contemp. Math. 341, 17--24 (2004; Zbl 1054.46027)], of \textit{M. Abel'} and \textit{A. Kokk} [Izv. Akad. Nauk Èst. SSR, Fiz., Mat. 37, No. 4, 377--386 (1988; Zbl 0677.46030)], or to the work [Topol. Algebra Appl. 2, 19--23 (2014; Zbl 1316.46040)] of \textit{E. Anjidani} could have been provided.