The Gelfand transform in commutative algebra

VM Buchstaber, A Lazarev

Research output: Contribution to journalArticle (Academic Journal)peer-review


We consider the transformation ev which associates to any element in a K-algebra A a function on the the set of its K-points. This is the analogue of the fundamental Gelfand transform. Both ev and its dual ev* are the maps from a discrete K-module to a topological K-module and we investigate in which case the image of each map is dense. This question arises in the classical problem of the reconstruction of a function by its values at a given set of points. The answer is nontrivial for various choices of K and A already for A=K[x], the polynomial ring in one variable. Applications to the structure of algebras of cohomology operations are given.
Translated title of the contributionThe Gelfand transform in commutative algebra
Original languageEnglish
Pages (from-to)7 - 23
Number of pages17
JournalMoscow Mathematical Journal
Volume5 (2)
Publication statusPublished - Apr 2005

Bibliographical note

Publisher: Independent University of Moscow


Dive into the research topics of 'The Gelfand transform in commutative algebra'. Together they form a unique fingerprint.

Cite this