Question: Abstract Algebra: Groups, Rings, and Fields: Introduce the basic algebraic structures of groups, rings, and fields, along with their axioms and properties. Discuss the connections

Abstract Algebra: Groups, Rings, and Fields: Introduce the basic algebraic structures of groups, rings, and fields, along with their axioms and properties. Discuss the connections between these structures and their applications in areas like cryptography

(

finite fields in public

-

key cryptography

)

or error

-

correcting codes

(

Galois fields

) .

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