Algebraic Structure in Mathematics

Authors

  • Mrs.Ravinder Msc. Mathemaics, LectureGSSS,Naguran

Keywords:

universal algebra, strong connections, modules, finitary operations

Abstract

In mathematics, and more specifically in abstract algebra, an algebraic structure is a set (called carrier set or underlying set) with one or more finitary operations defined on it that satisfies a list of axioms.[1] Examples of algebraic structures include groups, rings, fields, and lattices. More complex structures can be defined by introducing multiple operations, different underlying sets, or by altering the defining axioms. Examples of more complex algebraic structures include vector spaces, modules, and algebras. The properties of specific algebraic structures are studied in abstract algebra. The general theory of algebraic structures has been formalized in universal algebra. The language of category theory is used to express and study relationships between different classes of algebraic and non-algebraic objects. This because it is sometimes possible to find between some classes of objects, sometimes of different kinds. For example, Galois theory establishes a connection between certain fields and groups: two algebraic structures of different kinds.

References

Michel, Anthony N.; Herget, Charles J. (1993), Applied Algebra and Functional Analysis, New York: Dover Publications, ISBN 978-0-486-67598-5  Burris, Stanley N.; Sankappanavar, H. P. (1981), A Course in Universal Algebra, Berlin, New York: Springer-Verlag, ISBN 978-3-540-90578-3  Mac Lane, Saunders (1998), Categories for the Working Mathematician (2nd ed.), Berlin, New York: Springer-Verlag, ISBN 978-0-387-98403-2  Taylor, Paul (1999), Practical foundations of mathematics, Cambridge University Press, ISBN 978-0-521-63107-5

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Published

31-03-2017

How to Cite

Mrs.Ravinder. (2017). Algebraic Structure in Mathematics. International Journal for Research Publication and Seminar, 8(2), 72–78. Retrieved from https://jrps.shodhsagar.com/index.php/j/article/view/1018

Issue

Vol. 8 No. 2 (2017): Jan - Mar 2017

Section

Original Research Article

License

Copyright (c) 2017 International Journal for Research Publication and Seminar

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