Let S be a subring of the ring R. We investigate the question of whether S ∩ U(R) = U(S) holds for the units. In many situations our answer is positive. There is a special emphasis on the case when R is a full matrix ring and S is a structural subring of R defined by a reflexive and transitive relation.

Our main subject is to study the action of the Hecke operators Tl on the Jacobian J of the modular curve X0(N). We consider the Hecke algebra T, i.e. the subring of End(J) generated by the Tl and the involution ω and define the Eisenstein ideal I ⊂ T as the ideal generated by 1 +ω and 1 + l−Tl, l prime 6= N . The Eisenstein quotient of J is the quotient J̃ := J/aJ where a denotes the kernel of t...

Let N ⊂ Rr be a lattice, and let deg : N → C be a piecewise-linear function that is linear on the cones of a complete rational polyhedral fan. Under certain conditions on deg, the data (N, deg) determines a function f : H → C that is a holomorphic modular form of weight r for the congruence subgroup Γ1(l). Moreover, by considering all possible pairs (N, deg), we obtain a natural subring T (l) o...

In this paper, we confirm a conjecture of Alcántar by showing that graph subrings always admit standard Noether normalizations.

Abstract. We study the Z2-equivariant K-theory of M(A), where M(A) is the complement of the complexification of a real hyperplane arrangement, and Z2 acts on M(A) by complex conjugation. We compute the rational equivariant Kand KO-rings of M(A), and we give two different combinatorial descriptions of a subring Line(A) of the integral equivariant KO-ring, where Line(A) is defined to be the subri...

Abstract. We study the Z2-equivariant K-theory of M(A), where M(A) is the complement of the complexification of a real hyperplane arrangement, and Z2 acts on M(A) by complex conjugation. We compute the rational equivariant K and KO rings of M(A), and we give two different combinatorial descriptions of a subring Line(A) of the integral equivariant KO ring, where Line(A) is defined to be the subr...

In the early 1990’s, Kim and Roush developed path methods for establishing strong shift equivalence (SSE) of positive matrices over a dense subring U of R. This paper gives a detailed, unified and generalized presentation of these path methods. New arguments which address arbitrary dense subrings U of R are used to show that for any dense subring U of R, positive matrices over U which have just...