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In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations acting on their elements. [1] Algebraic structures include groups , rings , fields , modules , vector spaces , lattices , and algebras over a field .
Moderne Algebra has a rather confusing publication history, because it went through many different editions, several of which were extensively rewritten with chapters and major topics added, deleted, or rearranged. In addition the new editions of first and second volumes were issued almost independently and at different times, and the numbering ...
Éléments de mathématique is divided into books, volumes, and chapters.A book refers to a broad area of investigation or branch of mathematics (Algebra, Integration); a given book is sometimes published in multiple volumes (physical books) or else in a single volume.
The scope of algebra thus grew to include the study of algebraic structures. This object of algebra was called modern algebra or abstract algebra, as established by the influence and works of Emmy Noether. [36] Some types of algebraic structures have useful and often fundamental properties, in many areas of mathematics.
A Survey of Modern Algebra (with Garrett Birkhoff). A K Peters. ISBN 1-56881-068-7; 1948, "Groups, categories and duality," Proceedings of the Nat. Acad. of Sciences of the USA 34: 263–67. 1963. MacLane, Saunders (October 1963). "Natural Associativity and Commutativity". Rice Institute Pamphlet - Rice University Studies. hdl:1911/62865. 1995 ...
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Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.