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MATH 425 Exam 3 Guaranteed A+
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MATH 425 Exam 3 Guaranteed A+ Group ️Closed, Associative, Identity, Inverse One-to-one ️If f(x)=f(y), then x=y Onto ️For any element in the codomain, there is an element in the domain that maps to it Homomorphism ️Function that satisfies the property ø(xy) = ø(x) ø(y) Isomorphi...

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  • October 16, 2024
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  • 2024/2025
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MATH 425 Exam 3 Guaranteed A+

Group ✔️Closed, Associative, Identity, Inverse



One-to-one ✔️If f(x)=f(y), then x=y



Onto ✔️For any element in the codomain, there is an element in the domain that maps to it



Homomorphism ✔️Function that satisfies the property ø(xy) = ø(x) ø(y)



Isomorphism ✔️Homomorphism Property, One-to-one, Onto



Kernel ✔️Set of all elements in the domain that map to the identity in the codomain



Factor Group ✔️Let H be a normal subgroup of G. Then the cosets of H form a group G/H under the
binary operation (aH)(bH) = (ab)H. The group G/H is the factor or quotient group of G by H.



Ring ✔️Abelian group under +, associative under *, left distribution a(b+c) = ab + ac, and right
distribution (a + b)c = ac + bc



Commutative Ring ✔️Ring where multiplication is commutative



Ring with Unity ✔️Ring with a multiplicative identity



Unit ✔️An element in a ring that has a multiplicative inverse



Division Ring ✔️Ring where every nonzero element is a unit

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