Algebraic Structures I (Matrices, Groups, Rings, and Fields)
Rajesh Kumar Balakrishnan, Sriraman Sridharan · Discrete Mathematics · 2019
Algebraic structures encompass several structures-matrices, vector spaces, lattices, groups, rings, fields, categories and so on. They have a wide range of applications. To mention a few: Group theory has applications in physics and chemistry, ring theory in modeling databases, lattice theory for denotational semantics, program analysis and so on. (See also Abstract to Chapter 4 ). In this chapter on Algebraic Structures-I, we discuss the fundamental properties of the basic algebraic structures, namely, matrices, groups, subgroups, cyclic subgroups, rings, subrings, ideals, homomorphism and isomorphism between rings and finally fields.