2022•arXiv (Cornell University)Open access

Introduction into Noncommutative Algebra, Volume 1

Aleks Kleyn

Abstract

I dedicated the volume $1$ of monograph 'Introduction into Noncommutative Algebra' to studying of algebra over commutative ring. The main topics that I covered in this volume: definition of module and algebra over commutative ring; linear map of algebra over commutative ring; vector space over associative division algebra; system of linear equations over associative division algebra; homomorphism of vector space over associative division algebra and covariance theory; eigenvalue and eigenvector over associative division algebra.

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Key concepts: Division algebra, Associative algebra, Noncommutative geometry, Algebra over a field, Incidence algebra, Cellular algebra, Mathematics, Symmetric algebra