A completely primary finite ring is a ring R with identity 1 = 0 whose subset of all its zero divisors forms the unique maximal ideal J . Let R be a commutative completely primary finite ring with the unique maximal ideal J such that J3 = (0) and J2 = (0). Then R/J ∼= GF(pr) and the characteristic of R is pk, where 1≤ k ≤ 3, for some prime p and positive integer r. Let Ro =GR(pkr , pk) be a Gal...

We construct the intermediate coverings of cluster-tilted algebras by defining the generalized cluster categories. These generalized cluster categories are Calabi-Yau triangulated categories with fraction CY-dimension and have also cluster tilting objects (subcategories). Furthermore we study the representations of these intermediate coverings of cluster-tilted algebras.

In this paper we are interested in the following question: what is the smallest number of circuits, s(n,r), that is sufficient to determine every uniform oriented matroid of rank r on n elements? We shall give different upper bounds for s(n,r) by using special coverings called connected coverings. (~) 1998 Elsevier Science B.V. All rights reserved

Thin coverings are a method of constructing graded-simple modules from simple (ungraded) modules. After a general discussion, we classify the thin coverings of (quasifinite) simple modules over associative algebras graded by finite abelian groups. The classification uses the representation theory of cyclotomic quantum tori. We close with an application to representations of multiloop Lie algebras.

Branched coverings relate closed, orientable 3-manifolds to links in S, and open, orientable 3-manifolds to strings in S r T , where T is a compact, totally disconnected tamely embedded subset of S. Here we give the foundations of this last relationship. We introduce Fox theory of branched coverings and state the main theorems. We give examples to illustrate the theorems.

In this paper, uniform designs are constructed based on nearly U-type designs and the discrete discrepancy. The link between such uniform designs and resolvable packings and coverings in combinatorial design theory is developed. Through resolvable packings and coverings without identical parallel classes, many infinite classes of new uniform designs are then produced.

Évariste Galois (1811–1832) has been increasingly recognised as an important mathematician who despite his short life developed mathematical ideas that today have led to applications in computer science (such as Galois connections) and elsewhere. Some of Galois’ mathematics can be visualised in interesting and even artistic ways, aided using software. In addition, a significant corpus of the hi...

In the study of Galois theory, after computing a few Galois groups of a given field, it is very natural to ask the question of whether or not every finite group can appear as a Galois group for that particular field. This question was first studied in depth by David Hilbert, and since then it has become known as the Inverse Galois Problem. It is usually posed as which groups appear as Galois ex...

Given a ring A and an A-coring C we study when the forgetful functor from the category of right C-comodules to the category of right A-modules and its right adjoint − ⊗A C are separable. We then proceed to study when the induction functor − ⊗A C is also the left adjoint of the forgetful functor. This question is closely related to the problem when A → AHom(C, A) is a Frobenius extension. We int...

A stapled sequence is a set of consecutive positive integers such that no one of them is relatively prime with all of the others. The problem of existence and construction of stapled sequences of length N was extensively studied for over 60 years by Pillai, Evans, Brauer, Harborth, Erdös and others. Sivasankaranarayana, Szekeres and Pillai proved that no stapled sequences exist for any N < 17. ...