Euclidean ring is principle ideal R

Описание: Lecture 17: Every Euclidean ring is a principle ideal ring
Lecture 16: Fundamental theorem of homomorphism of ring    • Fundamental theorem of homo. of ring #divi...  
Every homomorphic image is isomorphic to its quotient ring
Lecture 15:Kernel of f, homomorphism    • kernel of f is an ideal of R| KERNEL #divi...  
If f is a homomorphism from R to R' then ker f is an ideal of R.
Lecture 14: Kernel of f
If f is a homomorphism from R to R' then ker f is an ideal of R.
Lecture 13: In Commutative ring with unity , I is a maximal ideal iff R/I is a field.    • In CRU I is maximal iff R/I is field #divi...  
Lecture 12: Field    • Field has only ideal{0} and F itself #divi...  
If F is a field then it has only two ideal {0} and F itself.
Lecture 11: Theorem : Ring of a Integer is a Principal Ideal Ring.    • Ring of integer is Principal IR| #divita #...  
Lecture 10 : Theorem: Union of two ideal is again an ideal of a ring iff it contain in one another.    • Union of two ideal is ideal| #divita #bsc_...  
Lecture 9: definition of Prime ideal    • intersection of two ideal is ideal| prime ...  
Theorem: intersection of two ideals of a ring is also an ideal of a ring.
Lecture 8: Definition of Principal Ideal
Definition of Maximal Ideal
Theorem: In ring of integer , ideal is maximal iff it is generated by prime integer.    • Maximal Ideal| Theorem #bsc_maths #abstrac...  
Lecture 7: Definition of an IDEAL
Theorem: if (R,+,.) is ring, S is non empty subset R, then S is an ideal of R iff
1. a-b belong to S
2. rs and sr belong to S    • IDEAL| one step test of ideal #bsc_maths #...  
Lecture 6: Definition of Ring Homomorphism
Definition of Ring Isomorphism
Theorem: In a Ring, Homomorphic image of commutative ring is commutative.    • in ring, homomorphic image of commutative ...  
Lecture 5: if R is a ring such that a^2=a for all a belong to R then
1. a+a=0 , for all a belong to R
2. a+b=0 imply a=b
3. R is a commutative ring    • every element is idempotent then ring is c...  
Lecture 4: Elementary properties of a Ring
1. a.0=0.a=0 for all a belong to ring
2. a.(-b)=(-a).b=-(a.b)
3. (-a).(-b)=-(a.b)    • Elementary properties of a ring| #Ringtheo...  
Lecture 3: Zero Divisor
Ring Without zero divisor
Cancellation law
A ring is without zero divisor iff it holds cancellation law.
   • zero divisor|without zero divisor|cancella...  
Lecture 2: prove set of integer is ring
rind w.r.t addition modulo, multiplication modulo    • prove a set is ring #Ringtheory |start new...  
lecture 1: Definition of Ring    • Definition of Ring #Ring theory |start new...  

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