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ABSTRACT ALGEBRA

  In  mathematics , more specifically  algebra ,  abstract algebra  or  modern algebra  is the study of  algebraic structures . [1]  Algebraic structures include  groups ,  rings ,  fields ,  modules ,  vector spaces ,  lattices , and  algebras over a field . The term  abstract algebra  was coined in the early 20th century to distinguish it from older parts of algebra, and more specifically from  elementary algebra , the use of  variables  to represent numbers in computation and reasoning. The abstract perspective on algebra has become so fundamental to advanced mathematics that it is simply called "algebra", while the term "abstract algebra" is seldom used except in  pedagogy .