Ring theory Notes, Mathematics, Handwritten notes

notations of ring
ring definition


difference between group and ring


 

null set form a smallest ring

commutative ring
ring theory




ring with unity

polynomial ring

division ring or skew field

cancellation law hold in Integral domain

integral domain hold in cancellation law

Field

A field is integral domain

Integral domain is not field

Ring homomorphism


counter example of ring homomorphism

ring isomorphism

example of ring isomorphism

Ideal definition, ideal contain a unit

ideal in R are <0> and itself

types of ideal, principal ideal, prime ideal

Examples and counter examples of ideal

Maximal ideal



lemma and theorem related to ideals

Quotient ring or factor ring

example of quotient ring and ideal

characteristic of a ring ,finite field

characteristic of field is zero or a prime number

relationship between commutative ring and field

 R/M is field

M is maximal ideal 

kernal f is ideal

1st theorem of isomorphism

first theorem of isomorphism part 2

2nd theorem of isomorphism

2nd theorem isomorphism part 2

2nd theorem of isomorphism part 3

fundamental theorem of ring homomorphism

fundamental theorem of isomorphim part 2

ring Z is trivial isomorphism with itself

Z is trivial isomorphism with itself part 2

zero divisor 

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