Question

Can anyone explain to me about:
i)ideals and why ideals allows us to construct quotient rings?

i)principal ideals,

ii)maximal ideals ,

iii)prime ideals ,

iv)Principal Ideal Domains

vi)Unique Factorisation Domain

Explicit explanation and perhaps examples could be helpful,Thanks

Answer 1

sol.

(1.) It is sain=d to be an ideal of R if

Ideas allow us to construct quotient rings, as coset multiplication becomes valid, as

but if we take subeing, then quotient ring is not possible as coset multiplication will not be well defined.

iii) P ideal is prime ideal of R if whenever

iv) in which each ideal is principle then R is said to be P.I.D.

Ideas allow us to construct quotient rings, as coset multiplication becomes valid, as

but if we take subeing, then quotient ring is not possible as coset multiplication will not be well defined.

iii) P ideal is prime ideal of R if whenever

iv) in which each ideal is principle then R is said to be P.I.D.