Lec2 Factorization Theory in integral Domain

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Lec2 Algebra 2nd M.Sc Mathematics punjab university in particular and other universities in General
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Factorization Theory in integral Domain

# Definition of PIR i.e. principal ideal ring

# Definition of PID i.e. Principal ideal Domain

#Types of Ideal

# Z, set of integer is PID

* Result which are used: Division Algorithm

# Field is PID
* Results
# If 1 belongs to ideal I ofa ring R then I=R
# Field has generator 1 i.e. F= <1>
And
# If be an ideal I of Field F then for every element  of has unit elements in F therefore for a €I there exists b€F such that ab=1

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Factorization Theory in integral Domain Lec 1st

Hello friends,
Lec 1 Algebra 2nd M.Sc Mathematics punjab university in particular and other universities in General

Click here to watch the lecture

Factorization Theory in integral Domain
Definition of Ideal

Definition of Ideal generated by Set S 

Definition of Principal ideal

Theorem: A commutative ring R and a belongings to R then principal ideal <a>={ar+na: r€R, n€Z }

Cor: A commutative ring with unity and a belongings to R then principal ideal  <a>=aR=Ra

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