Math 4045/5045: Advanced Algebra I

Fall 2017, Dalhousie University

Time and location: Mondays, Wednesdays & Fridays 11:35--12:25 pm in Chase 227.

Office hours: Tuesdays 10--11 am & Wednesdays 1:30--2:30 pm in Chase 314.

Course Syllabus: can be found here.

Theorems for Final Exam: can be found here.

Homework: Homework:

 Homework Problems Due Date HW#1 Chapter III Section 2: 13, 18, 21; Chapter IV Section 1: 2, 3 Wednesday Sept 20 HW#2 Chapter IV Section 1: Write proofs for theorems 1.11, 1.12, 1.13; Exercises: 4, 13 Wednesday Sept 27 HW#3 Chapter IV Section 2: 1, 4, 7 Wednesday Oct 4 HW#4 Chapter IV Section 1: 11; Section 2: 2.10, 2.12; Section 6: 6.2, 6.4; Wednesday Oct 18 HW#5 Chapter IV Prove Proposition 3.7 and do Section 3: 2, 5, 6, 9, 12 Wednesday Nov 15 HW#6 Chapter IV Prove Theorem 4.7 and do Section 4: 1, 9,11 Wednesday Nov 29 HW#7 Chapter IV Section 5: 1, 2, 3, 4, 6, 7 Tuesday Dec 5

Calendar:

 Date Topics Covered W Sep 6 Reviewed rings and ideals (Chapter III) F Sep 8 Definitions of categories, modules and submodules M Sep 11 Homomorphisms, Hom, and quotient modules W Sep 13 Module Isomorphism Theorems F Sep 15 Generators of modules M Sep 18 Exact Sequences W Sep 20 Split exact sequences F Sep 22 Free modules M Sep 25 More on free modules W Sep 27 vector spaces: free modules over division rings F Sep 29 Started discussin on rank M Oct 2 Rank of free modules over division rings W Oct 4 Invariant rank property F Oct 6 Noetherian modules, Torsion modules M Oct 9 THANKSGIVING-- NO CLASS W Oct 11 Modules over PIDs F Oct 13 Modules over PIDs M Oct 16 Modules over PIDs W Oct 18 Modules over PIDs F Oct 20 Modules over PIDs M Oct 23 MIDTERM W Oct 25 Projective modules F Oct 27 Projective modules and injective modules M Oct 30 Baer's criterion and divisible modules T Oct 31 [LAST DAY TO DROP WITH W] NO CLASS W Nov 1 Injective modules F Nov 3 Every module over a ring with identity is contained in an injective one M Nov 6 STUDY BREAK -- NO CLASS W Nov 8 STUDY BREAK -- NO CLASS F Nov 10 STUDY BREAK -- NO CLASS M Nov 13 REMEMBRANCE DAY -- NO CLASS W Nov 15 Hom is left exact F Nov 17 Special cases when Hom is also right exact; bimodules M Nov 20 Duality W Nov 22 Reflexive modules F Nov 24 Tensor products of modules M Nov 27 Module structure on tensor products W Nov 29 F Dec 1 M Dec 4 T Dec 5 LAST DAY -- MONDAY SCHEDULE