Algebraic Theories

Dover Publications, 1959. First Softcover Edition . Soft cover. Very Good. Ix, 276 Pp. + Catalog At End. First Softcover Printing, Unlaminated Cover Priced $1.50. Slight Usage, Minimal Rubbing To Edges. Per Wikipedia, Leonard Eugene Dickson (1874 -1954) Was An American Mathematician. He Was One Of The First American Researchers In Abstract Algebra. In 1896, When He Was Only 22 Years Of Age, He Was Awarded Chicago's First Doctorate In Mathematics, For A Dissertation Titled The Analytic Representation Of Substitutions On A Power Of A Prime Number Of Letters With A Discussion Of The Linear Group, Supervised By E. H. Moore. Dickson Then Went To Leipzig And Paris To Study Under Sophus Lie And Camille Jordan, Respectively. Chicago Offered Him A Position In 1900, And He Spent The Balance Of His Career There. At Chicago, He Supervised 53 Ph.D. Theses; His Most Accomplished Student Was Probably A. A. Albert. Dickson Was The First Recipient Of A Prize Created In 1924 By The American Association For The Advancement Of Science, For His Work On The Arithmetics Of Algebras. Dickson Presided Over The American Mathematical Society In 1917-1918. His December 1918 Presidential Address, Titled "Mathematics In War Perspective", Criticized American Mathematics For Falling Short Of Those Of Britain, France, And Germany: Dickson Had A Major Impact On American Mathematics, Especially Abstract Algebra. His Mathematical Output Consists Of 18 Books And More Than 250 Papers. The Collected Mathematical Papers Of Leonard Eugene Dickson Fill Six Large Volumes. In 1901, Dickson Published His First Book Linear Groups With An Exposition Of The Galois Field Theory, A Revision And Expansion Of His Ph.D. Thesis. Parshall (1991) Described The Book As Follows: "Dickson Presented A Unified, Complete, And General Theory Of The Classical Linear Groups-Not Merely Over The Prime Field Gf(P) As Jordan Had Done-But Over The General Finite Field Gf(Pn), And He Did This Against The Backdrop Of A Well-Developed Theory Of These Underlying Fields. ... His Book Represented The First Systematic Treatment Of Finite Fields In The Mathematical Literature." An Appendix In This Book Lists The Non-Abelian Simple Groups Then Known Having Order Less Than 1 Billion. He Listed 53 Of The 56 Having Order Less Than 1 Million. The Remaining Three Were Found In 1960, 1965, And 1967. Dickson Worked On Finite Fields And Extended The Theory Of Linear Associative Algebras Initiated By Joseph Wedderburn And Cartan. He Started The Study Of Modular Invariants Of A Group. In 1905, Wedderburn, Then At Chicago On A Carnegie Fellowship, Published A Paper That Included Three Claimed Proofs Of A Theorem Stating That All Finite Division Algebras Were Commutative, Now Known As Wedderburn's Theorem. The Proofs All Made Clever Use Of The Interplay Between The Additive Group Of A Finite Division Algebra A, And The Multiplicative Group A* = A ? [0]. Karen Parshall Noted That The First Of These Three Proofs Had A Gap Not Noticed At The Time. Dickson Also Found A Proof Of This Result But, Believing Wedderburn's First Proof To Be Correct, Dickson Acknowledged Wedderburn's Priority. But Dickson Also Noted That Wedderburn Constructed His Second And Third Proofs Only After Having Seen Dickson's Proof. She Concluded That Dickson Should Be Credited With The First Correct Proof. Dickson's Search For A Counterexample To Wedderburn's Theorem Led Him To Investigate Nonassociative Algebras, And In A Series Of Papers He Found All Possible Three And Four-Dimensional (Nonassociative) Division Algebras Over A Field. The Three-Volume History Of The Theory Of Numbers (1919-23) Is Still Much Consulted Today, Covering Divisibility And Primality, Diophantine Analysis, And Quadratic And Higher Forms. The Work Contains Little Interpretation And Makes No Attempt To Contextualize The Results Being Described, Yet It Contains Essentially Every Significant Number Theoretic Idea From The Dawn Of Mathematics Up To The 1920S Except For Quadratic Reciprocity And Higher Reciprocity Laws.