Algebras and their arithmetics

by: Dickson, Leonard E. (Leonard Eugene), 1874-1954

Publication date: 1923

Topics: Algebra, Universal, algebrai struktúrák, algebrai struktúrák

Publisher: Chicago, Ill. : University of Chicago Press

Collection: mitlibrariespublicdomain; mitlibraries; americana

Digitizing sponsor: MIT Libraries

Contributor: MIT Libraries

Language: English

xii, 241 pages ; 20 cm

Includes index

Introduction, definitions of algebras, illustrations -- Linear sets of elements of an algebra -- Invariant sub-algebras, direct sum, reducibility, difference algebras -- Nilpotent and semi-simple algebras; idempotent elements -- Division algebras -- Structure of algebras -- Characteristic matrices, determinants, and equations; minimum and rank equations -- The principal theorem on algebras -- Integral algebraic numbers -- The arithmetic of an algebra -- Fields -- Appendix I. Division algebras of order n² -- II. Determination of all division algebras of order 9; miscellaneous general theorems on division algebras -- III. Statement of further results and unsolved problems