
Recent Posts
Recent Comments
vfp15 on Group Theory I.4 (Conjugate… limsup on Group Theory I.3 (Order of a… Ang Yan Sheng on Group Theory I.3 (Order of a… Archives
Categories
Meta
Tag Archives: algebra
Basic Algebra I.5 (Operations on Ideals)
Given ideals I and J of ring R, we can perform the following operations to obtain new ideals: is an ideal of R; is an ideal of R; is an ideal of R. Thus, IJ is the set of all … Continue reading
Posted in Basic Algebra Notes
Tagged abstract algebra, algebra, basic course, notes, ring theory, undergraduate
Leave a comment
Basic Algebra I.4 (Ideals and Ring Quotients)
Our first naïve attempt is to take a ring quotient R/S for a subring S of R. First, (S, +) is a subgroup of (R, +) so we can denote every coset R/S by x+S for some x in R. … Continue reading
Posted in Basic Algebra Notes
Tagged abstract algebra, algebra, basic course, notes, ring theory, undergraduate
Leave a comment
Basic Algebra I.3 (Subrings and Ring Products)
The concept of subrings follow naturally. Let R be a ring. A subring is a subset S of R such that: (S, +) is a subgroup of (R, +); S contains 1; for any a, b in S, ab is … Continue reading
Posted in Basic Algebra Notes
Tagged abstract algebra, algebra, basic course, notes, ring theory, undergraduate
Leave a comment
Basic Algebra I.2 (Examples + Basic Properties of Rings)
Examples The set Z of integers forms a ring under addition and multiplication, but the subset 2Z of even integers forms a rng. The set Z/nZ of integers modulo n forms a ring under addition and multiplication mod n. We have rings Q, R and C, which are … Continue reading
Posted in Basic Algebra Notes
Tagged abstract algebra, algebra, basic course, notes, ring theory, undergraduate
Leave a comment
Basic Algebra I.1 (Enter the Rings)
In this series, we will cover some common algebraic structures – other than groups, which had been amply covered in the Group Theory series. However, due to the considerable depth of many of the topics, we can only provide a brief … Continue reading
Posted in Basic Algebra Notes
Tagged abstract algebra, algebra, basic course, notes, ring theory, undergraduate
Leave a comment
Group Theory ∞ (Epilogue)
That concludes the end of the series of notes on Group Theory. Has it been successful? I don’t know, but I’m reasonably pleased with the way the notes turn out, except the fact that there’s a huge disparity between the … Continue reading
Posted in Group Theory Notes
Tagged abstract algebra, algebra, basic course, epilogue, group theory, notes, undergraduate
Leave a comment
Group Theory XII.5 (More Category Theory)
Since a category is really a bunch of abstract objects and arrows between them, we can reverse them by duality. Let C be a category. The opposite category Cop is the category such that: Ob(Cop) = Ob(C); for any objects … Continue reading
Posted in Group Theory Notes
Tagged abstract algebra, algebra, basic course, group theory, notes, undergraduate
Leave a comment