\(SK_ 1\) of an interesting principal ideal domain. (English) Zbl 0467.18004

Grayson, Daniel R.

J. Pure Appl. Algebra 20, 157-163 (1981).

MSC:

18F25	Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)
37D15	Morse-Smale systems
18F30	Grothendieck groups (category-theoretic aspects)
13D15	Grothendieck groups, \(K\)-theory and commutative rings
16E20	Grothendieck groups, \(K\)-theory, etc.

Keywords:

principal ideal domain; Morse-Smale diffeomorphism; higher algebraic K- theory

References:

[1]	Bass, H., Algebraic K-theory, (1968), Benjamin New York · Zbl 0174.30302
[2]	Bass, H., The Grothendieck group of the category of abelian group automorphisms of finite order, (1979), Columbia University, Preprint
[3]	H. Bass, Lenstra’s calculations of G0(R[π]), and applications to Morse-Smale diffeomorphisms in, Orders and their applications, Springer Lectures Notes (to appear).
[4]	J. Franks and M. Shub, The existence of Morse-Smale diffeomorphisms, Topology (to appear). · Zbl 0472.58013
[5]	Grayson, D., The K-theory of endomorphisms, J. algebra, 48, 439-446, (1977) · Zbl 0413.18010
[6]	Lenstra, H.W., Grothendieck groups of abelian group rings, J. pure appl. algebra, 20, 173-193, (1981), (this issue). · Zbl 0467.16016
[7]	Smale, S., Differentiable dynamical systems, Bull. AMS, 73, 747-817, (1967) · Zbl 0202.55202
[8]	Shub, M.; Sullivan, D., Homology theory and dynamical systems, Topology, 14, 109-132, (1975) · Zbl 0408.58023
[9]	Quillen, D., Higher algebraic K-theory I, () · Zbl 1198.19001