Blogs about: 305 Abstract Algebra I
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305 -Homework set 9
[Update: I added an additional assumption to question 3.] This set is due May 13 at 10:30 am. Remember that we will have an additional meeting that day. Details of the homework policy can be found on … more →
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305 -Homework set 9
wrote 8 months ago: [Update: I added an additional assumption to question 3.] This set is due May 13 at 10:30 am. Rememb … more →
305 -Homework set 8
wrote 8 months ago: This set is due May 1 at the beginning of lecture. Details of the homework policy can be found on th … more →
305 -9. Groups
wrote 8 months ago: We want to define the notion of group that will be fundamental to determine which polynomials are so … more →
305 -8. Irreducibility
wrote 8 months ago: In this lecture I want to present a couple of short results that are nevertheless very useful in pra … more →
305 -Extension fields revisited (3)
wrote 8 months ago: 1. Isomorphisms We return here to the quotient ring construction. Recall that if is a commutative ri … more →
305 -Extension fields revisited (2)
wrote 8 months ago: Most of our work from now on depends on the following simple, but very useful observation: Theorem 1 … more →
305 -7. Extension fields revisited
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wrote 9 months ago: 1. Greatest common divisors. Let’s conclude the discussion from last lecture. If is a fiel … more →
305 -Homework set 7
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wrote 9 months ago: This set is due April 10 at the beginning of lecture. Details of the homework policy can be found on … more →
305 -Homework set 6
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wrote 9 months ago: This set is due April 3 at the beginning of lecture. Details of the homework policy can be found on … more →
305 -Rings, ideals, homomorphisms (3)
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wrote 9 months ago: In order to understand the construction of the quotient ring from last lecture, it is convenient to … more →
305 -Rings, ideals, homomorphisms (2)
wrote 9 months ago: Let’s begin by verifying: Theorem 1 If are rings and is a homomorphism, then is an ideal of … more →
305 -6. Rings, ideals, homomorphisms
wrote 9 months ago: It will be important to understand the subfields of a given field; this is a key step in figuring ou … more →
305 -Extensions by radicals (3)
wrote 10 months ago: 3. Examples Last lecture we defined what it means that a polynomial with coefficients in a field … more →
305 -Extensions by radicals (2)
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wrote 10 months ago: 2. Extensions by radicals Last lecture we defined where is a subfield of a field all the roots of … more →
305 -Homework set 5
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wrote 10 months ago: This set is due March 11 at the beginning of lecture. Details of the homework policy can be found on … more →
305 -5. Extensions by radicals
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wrote 10 months ago: (This post was typeset using Luca Trevisan’s LaTeX2WP program.) Last lecture we characterized … more →
305 -Fields (5)
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wrote 10 months ago: At the end of last lecture we stated a theorem giving an easy characterization of subfields of a giv … more →
305 -Homework set 4
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wrote 10 months ago: I am not happy with the solutions I received for problems 4 and 5 of Homework set 2 so, for this new … more →
305 -Fields (4)
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wrote 10 months ago: Suppose that is a field and that It may be that is also a field, using the same operations of For ex … more →
