ABSTRACT
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.
