Abstract Algebra Dummit Pdf

Abstract algebra deals with the study of algebraic structures. Those structures are sets and their collections of operations, which are defined on them. Abstract algebra encompasses the study of polynomial rings and ideals, groups, rings of sets, vector spaces, matrices over a fixed field, modules over a fixed ring, and algebras over a fixed field. The techniques and concepts of abstract algebra are used in number theory and the theory of groups. In these areas, abstract algebra is known as “particular algebra”.

 

Abstract algebra is a generalization of the familiar arithmetic of whole numbers, real numbers and complex numbers. Abstract algebra developed during the late 19th and early 20th centuries, mostly as a result of work by G. Peano, G. Frege and others. It contains such basic objects as integers, rational numbers, real numbers, and further extensions to generalize solutions of polynomial equations with integer coefficients in any number of variables. The formalism used for this process depends on axiomatic systems with specific sets of primitive symbols and rules using them. Abstract algebra has been particularly successful in describing mathematical structures underlying other areas of mathematics (such as geometry), traditional areas of mathematical physics (such as statics and mechanics) and computer science (such as the semantics of programming languages).

 

Abstract algebra is an important subject for students of mathematics, theoretical computer science, and certain areas of modern physics. This free on-line resource publishes major monographs (books) from the leading textbook authors in this area.