# Algebra Learning Seminar

Monday, July 27, 2015 — 1:30 PM EDT

Ehsaan Hossain, Pure Mathematics, University of Waterloo

"The Invariant Basis Number Property"

In linear algebra, the "dimension'' of a vector space can be defined uniquely --- every vector space has a basis, and all bases have the same cardinality. But this is a special advantage of working over a field. What about modules over a general ring $R$? It's possible that an $R$-module does not possess a basis, and even if it does, there may be bases of different cardinalities. In fact there is an easy example of a module possessing a basis is of cardinality $n$, for all $n\in \mathbf{N}$. Can we find an example of an $R$-module with bases of cardinality 2 and 3, but not 5? How far can we push this? We will see a group, called $K_0(R)$, which encodes this information (at least partially). I also hope to convince you that this investigation leads inevitably to the invention of Leavitt path algebras.

Location
MC 5479

,

### December 2021

S M T W T F S
28
29
30
4
5
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
1
1. 2021 (135)
1. December (11)
2. November (22)
3. October (15)
4. September (5)
5. August (15)
6. July (17)
7. June (15)
8. May (1)
9. April (4)
10. March (11)
11. February (9)
12. January (10)
2. 2020 (103)
1. December (10)
2. November (12)
3. October (4)
4. September (3)
5. August (1)
6. July (5)
7. June (1)
8. May (3)
9. March (16)
10. February (26)
11. January (22)
3. 2019 (199)
4. 2018 (212)
5. 2017 (281)
6. 2016 (335)
7. 2015 (211)
8. 2014 (235)
9. 2013 (251)
10. 2012 (135)