On Algebraic Integral

We generalize the notion of integration from analysis to monoid actions, establish a representation of regular integrals by bijective crossed-homomorphisms, provide a complete classification of regular integrals over the real numbers, and develop an algebraic method of integration.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-05-31
DOI
https://doi.org/10.5281/zenodo.20468842
Primary Topic
Homotopy and Cohomology in Algebraic Topology
Type
preprint
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preprint

On Algebraic Integral

Nikita Umerov
Zenodo (CERN European Organization for Nuclear Research)
Homotopy and Cohomology in Algebraic Topology
preprint

On Algebraic Integral

Nikita Umerov
preprint en

Abstract

We generalize the notion of integration from analysis to monoid actions, establish a representation of regular integrals by bijective crossed-homomorphisms, provide a complete classification of regular integrals over the real numbers, and develop an algebraic method of integration.

Zenodo (CERN European Organization for Nuclear Research)
Reduced inequalities
Homotopy and Cohomology in Algebraic Topology
DOIOpen Access PDFOpenAlex
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On Algebraic Integral — Nikita Umerov · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS