Date
|
Material
covered
|
10 Oct
|
Chapter
3 sections 2,3,4
|
3 Oct
|
Chapter 1, section 11;
Chapter 3, section 117
Categories and functors were discused. For a fixed commutative ring R,
the group ring construction G--> R[G] was shonw to be a functor from
the category of groups to the category of R algebras. In the saim vain
it was shown that for a fixed group G, the group ring construction
R-->R[G] is also a functor between
the category of commutative rings to the cateogry of rings.
The basic definitions related modules were presented
|
26 Sept
|
Chapter 2, section 107
We talked about localization of a ring with respect to multiplicative
systems.
|
| 19 Sept |
I plan to talk about
commutative rings (section 2 of chapter 2), maximal and prime ideals, I
will talk about theorem 2.1 and corollary 2.2. I will introduce a
categorical definition of a product. I plan to talk about localization
(section 4 of chapter 2). I would like also to talk about modules over
rings.
|
12 Sept
|
Chapter
2 section 1, 2 and 3
We continued talking about
group rings. We discussed ideals and operations on them. It was
shown that the ring of integers and polynomial ring over a field are
P.I.D's (all ideals are singly generated). Characteristic of a
ring was defined.
|
5 Sept
|
Chapter
2, section 1,2 and 3.
In the class we talked about
rings and algebras over a fixed commutative ring R:
an algebra is a ring homomorphism f between R and S such that for any r
in R and any s in S, f(r)s=sf(r) (the elements in R commute with those
in S).
Language of categories was introduced. Several examples were presented:
the ring of integers, the fields of rational, real and complex numbers,
Z/n, the algebra of matrices over a commutative ring and the group
algebra.
|
|
