Year: 2012
Type: preprint
Abstract: Groups preserving a distributive product are encountered often in algebra. Examples include automorphism groups of associative and nonassociative rings, classical groups, and automorphism groups of p-groups. While the great variety of such products precludes any realistic hope of describing the general structure of the groups that preserve them, it is reasonable to expect that insight may be gained from an examination of the universal distributive products: tensor products. We give a detailed description of the groups preserving tensor products over semisimple and semiprimary rings, and present effective algorithms to construct generators for these groups. We also discuss applications of our methods to algorithmic problems for which all currently known methods require an exponential amount of work.
Source: arXiv (Cornell University)
Authors: Brooksbank, Peter A., Wilson, James B.
Institutions: Bucknell University, Colorado State University
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2951205745