This paper investigates the arithmetic of fractional ideals and the infrastructure of the principal ideal class of a purely cubic function eld of unit rank one. We rst describe how irreducible polynomials split into prime ideals in purely cubic function elds of nonzero unit rank. This decomposition behavior is used to compute so-called canonical bases of fractional ideals; such bases are very s...

We introduce the concept of topological finite-determinacy for germs analytic functions within a fixed ideal I, which provides a notion of topological finite-determinacy of functions with non-isolated singularities. We generalize classical results of Thom and Varchenko stating the following: let A be the complement in the ideal I of the space of germs whose topological type remains unchanged un...

In this paper, we present a characteristic set method for mixed differential and difference polynomial systems. We introduce the concepts of coherent, regular, proper irreducible, and strongly irreducible ascending chains and study their properties. We give an algorithm which can be used to decompose the zero set for a finitely generated differential and difference polynomial sets into the unio...

Example. Let X be an algebraic projective irreducible surface over a field k and let P be a closed point of X , C ⊂ X be an irreducible curve such that P ∈ C . If X and C are smooth at P , then we let t ∈ OX,P be a local equation of C at P and u ∈ OX,P be such that u|C ∈ OC,P is a local parameter at P . Denote by C the ideal defining the curve C near P . Now we can introduce a two-dimensional l...

The distribution of ideal class groups of Fq(T, √ M(T )) is examined for degree-four monic polynomials M ∈ Fq[T ] when Fq is a finite field of characteristic greater than 3 with q ∈ [20000, 100000] or q ∈ [1020000, 1100000] and M is irreducible or has an irreducible cubic factor. Particular attention is paid to the distribution of the p-Sylow part of the class group, and these results agree wit...

We show that the maximal subgroup of the free profinite semigroup associated by Almeida to an irreducible sofic shift is a free profinite group, generalizing an earlier result of the second author for the case of the full shift (whose corresponding maximal subgroup is the maximal subgroup of the minimal ideal). A corresponding result is proved for certain relatively free profinite semigroups. W...

For a compact, orientable, irreducible, ∂-irreducible, and an-annular 3-manifold, it is shown there are only finitely many boundary slopes for incompressible ∂-incompressible surfaces of bounded Euler characteristic. We use normal surface theory the inverse relationship crushing triangulation along [8] that inflating an ideal [12] to introduce study boundary-efficient triangulations end-efficie...

We study the structure of 0-primitive near-rings and are able to answer an open question in the theory of minimal ideals in near-rings to the negative, namely if the heart of a zero symmetric subdirectly irreducible near-ring is subdirectly irreducible again. Also, we will be able to classify when a simple near-ring with an identity and containing a minimal left ideal is a Jacobson radical near...

Let o be a complete discrete valuation domain with finite residue field. In this paper we describe the irreducible representations of the groups Aut(M) for any finite o-module M of rank two. The main emphasis is on the interaction between the different groups and their representations. An induction scheme is developed in order to study the whole family of these groups coherently. The results ob...

We study conditions on a C∗-dynamical system (A,G,α) under which induction of primitive ideals (resp. irreducible representations) from stabilizers for the action of G on the primitive ideal space Prim(A) give primitive ideals (resp. irreducible representations) of the crossed product A⋊α G. The results build on earlier results of Sauvageot [17] and others, and will correct a (possibly overly o...