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Week
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Topics
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Study Metarials
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1
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Definition and Examples of ring
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R1- Section 3.1
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2
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Basic properties and Definitions (Integral domains, Characteristic of a ring, Division Ring, Field, Zero Divisor)
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R1- Section 3.3, Section 3.4
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3
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Subrings
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R1- Section 3.2
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4
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Ideals
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R1- Section 3.5
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5
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Quotient rings
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R1- Section 3.5
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6
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Homomorphisms and Isomorphisms
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R1- Section 3.6
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7
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Prime and Maximal Ideals
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R2- Section 4.8
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8
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Direct Sum of Rings
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SR2- Section 3.2
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9
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Polynomial Rings
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R1- Section 4.1
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10
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Euclidean Domains
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R1- Section 4.9, R1- Section 4.6
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11
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Prime and Irreducible Elements
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R2- Section 4.6
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12
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Unique Factorization Domain
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R2- Section 4.6
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13
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Factorization of Polynomials over UFD
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R1- Section 4.6, R2- Section 4.7
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14
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Irreducibility of Polynomails
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R1- Section 4.7
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