toanhoc

Let K_0 be the first algebraic K-theory group, Z[x] be the polynomial ring over the integers. What is K_0(Z[x]) ?
Actually, I want to know if it is zero or not ?
Is there a short exact sequence to relate K_0(Z), K_0(Z[x,x^{-1}]) and K_0(Z[x]) ?

Có ai có bản ebooks của J. Frank Adams không nhỉ ? Tôi muốn tìm mấy quyển này, đặc biệt là Vol. 2.
Cảm ơn.

http://www.eatcs.org.../citation08.pdf
The citation for the Godel prize this year looks extremely interesting. We learn algorithms complexity from the first course on algorithms and data structures and we are told that complexity should tell us how fast the algorithms runs. Unfortunately, this is true only theoretically. Even the average case does not predict well the algorithms in reality. The prize winners this year developed a method to understand the seem-to-be wild behaviour of algorithms. The example is the simplex method which is basic but very effective in optimization.

I am wondering if anyone can give me a quick tutor on BString, MString... ? Is that String topology ? Is that supposed to classify String structures on vector bundles ? And what is a string structure by the way ? From what I'm looking at now. A string structure implies a spin structure, implies an orỉented bundle.
Thanks in advance.

Một PID có homological dimension=projective dimension=1. Thế có kết quả gì cho Noetherian ring không nhỉ ? Lấy vành đa thức trên trường chẳng hạn. Có ví dụ nào tiêu biểu tôi nên ghi nhớ ?
Ví dụ mấy cái dim này khác nhau ?