Let F be a field of characteristic zero and let ft,n be the stabilization homomorphism from the nth integral homology of SLt(F ) to the nth integral homology of SLt+1(F ). We prove the following results: For all n, ft,n is an isomorphism if t ≥ n+ 1 and is surjective for t = n, confirming a conjecture of C-H. Sah. fn,n is an isomorphism when n is odd and when n is even the kernel is isomorphic ...

Let R ⊂ S and S ⊂ T be minimal ring extensions of (commutative) rings. If (i) each of these extensions is integral or (ii) each of these extensions is integrally closed or (iii) R ⊂ S is integral while S ⊂ T is integrally closed, then each chain of rings between R and T is finite. Examples are given of minimal extensionsR ⊂ S and S ⊂ T such thatR ⊂ S is integrally closed, S ⊂ T is any of the th...

We extend the work which has appeared in papers on sharp characters and originated with Blichfeldt and Maillet to the Burnside ring of a finite group G. We show that the polynomial whose zeros are the set of marks of non-identity subgroups on a faithful G-set X evaluated at X is an integral multiple of the regular G-set, and deduce a result about the size of a base of X . Further consequences f...

Let ZG be the integral group ring of the finite nonabelian group G over the ring of integers Z, and let ∗ be an involution of ZG that extends one of G. If x and y are elements of G, we investigate when pairs of the form (uk,m(x), uk,m(x ∗)), or (uk,m(x), uk,m(y)), formed respectively by Bass cyclic and ∗-symmetric Bass cyclic units, generate a free noncyclic subgroup of the unit group of ZG. 1....

In this paper we prove that if G is a finite group of automorphisms of a ring R, where the order of G is a unit in R, then R is fully integral of degree m(|G|) over the fixed ring R. Here m is a function of the order of G. This gives a positive answer to a well-known question of S. Montgomery and extends the result of D. S. Passman for abelian group actions. Our theorem can be viewed as a gener...

Title of thesis: CLASSIFICATION OF PRIME IDEALS IN INTEGRAL GROUP ALGEBRAS OF FINITE ABELIAN GROUPS Heather Mallie McDonough, Master of Arts, 2005 Thesis directed by: Professor William Adams Department of Mathematics Let Z[G] be the integral group algebra of the group G. In this thesis, we consider the problem of determining all prime ideals of Z[G] where G is both finite and abelian. Because o...