Algebraic structure

ALGEBRAIC STRUCTURE

Gà a non-empty set.

G with one or more binary operations is known as algebraic structures.

For examples:

1)  (G, *) , where ‘*’ is an binary operation on Set/Group ‘G’. Than (G,*) is an algebraic group.

2)  (N, +), where ‘+’ is an binary operation on Set/Group ‘N’,set of natural numbers.

3)  (I, + ), where ‘+’ is an binary operation on Set/Group ‘I’, set of integer numbers.

4)  (I, - ), where ‘-‘ is an binary operation on Set/Group ‘I’, set of integer numbers.

5)  (R, +, *), where ‘ + ‘ and  ‘ * ‘ are two binary operations on Set/Group ‘R’, set of real numbers.

6)  (R, +, .)

7)  (I, +, .) etc.



Properties of an Algebraic Structure:

1)      Associative and Commutative Laws:

(a * b)* c = a * (b * c)

(a * b ) = (b * a)


2)      Identity element and Inverses:

a * e = e * a = a, where e à identity element

Left identity element,
e * a = a.

Right identity element,
a * e = a.

If an binary operation ‘ * ‘ is not having an identity element,
Than,
inverse of an element ‘a’ in set is ‘b’.

a * b = b * a = e


3)      Cancellation Laws:

Left cancellation law:
a * b = a * c, implies b = c ( ‘a’ of both sides get cancelled).

Right cancellation law:

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Practicals:
Previous years solved papers:
A list of Video lectures References:
  1. Sebesta,”Concept of programming Language”, Pearson Edu 
  2. Louden, “Programming Languages: Principles & Practices” , Cengage Learning 
  3. Tucker, “Programming Languages: Principles and paradigms “, Tata McGraw –Hill. 
  4. E Horowitz, "Programming Languages", 2nd Edition, Addison Wesley

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    8. Register in Assembly Language Programming
    9. Arrays in Assembly Language Programming

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    2. Douglas E Comer, “Internetworking with TCP/IP Principles, Protocols, And Architecture",Pearson Education
    3. KavehPahlavan, Prashant Krishnamurthy, “Networking Fundamentals”, Wiley Publication.
    4. Ying-Dar Lin, Ren-Hung Hwang, Fred Baker, “Computer Networks: An Open Source Approach”, McGraw Hill.