If L is a field and R a subring of L, we define the lattice Val(L,R) as the lattice generated by symbols VR(s) for s in L with the relations 1. 1 = VR(r) if r is in R 2. VR(s) ∧ VR(t) 6 VR(s+ t) 3. VR(s) ∧ VR(t) 6 VR(st) 4. 1 = VR(s) ∨ VR(s) if s 6= 0 Contrary to the Zariski lattice, we cannot in general simplify an expression VR(s1) ∧ . . . ∧ V (sn) to a single basic open VR(s). Two exceptions...

Suppose D is an integral domain with quotient eld K and that L is an extension eld of K. We show in Theorem 4 that if the complete integral closure of D is an intersection of Archimedean valuation domains on K, then the complete integral closure of D in L is an intersection of Archimedean valuation domains on L; this answers a question raised by All rings considered in this paper are assumed to...

We show that a modified variant of the interior point method can solve linear programs (LPs) whose coefficients are real numbers from a subring of the algebraic integers. By defining the encoding size of such numbers to be the bit size of the integers that represent them in the subring, we prove the modified algorithm runs in time polynomial in the encoding size of the input coefficients, the d...

*Correspondence: [email protected] School of Mathematics Science, Liaocheng University, Liaocheng, Shandong 252059, China Abstract In order to generalize the notions of a (∈,∈ ∨q)-fuzzy subring and various (∈,∈ ∨q)-fuzzy ideals of a ring, a (λ,μ)-fuzzy subring and a (λ,μ)-fuzzy ideal of a ring are defined. The concepts of (λ,μ)-fuzzy semiprime, prime, semiprimary and primary ideals are introdu...

We prove the following generalization of the classical ShephardTodd-Chevalley Theorem. Let G be a finite group of graded algebra automorphisms of a skew polynomial ring A := kpij [x1, · · · , xn]. Then the fixed subring A has finite global dimension if and only if G is generated by quasireflections. In this case the fixed subring A is isomorphic a skew polynomial ring with possibly different pi...

If JR is a ring, and G is a group of automorphisms of R, then R denotes the subring of R consisting of elements of R left fixed by every element of G, and is called the Galois subring corresponding to G. In his paper, Groups acting on hereditary rings, G. M. Bergman has asked if every Galois subring of a right Ore domain corresponding to a finite group is itself right Ore. In this note we show ...

Consider a redundant ring network where each node is also connected to the nodes at distance d. In the presence of faulty nodes, the goal of a reconfiguration scheme is to construct the largest subring among the non-faulty nodes using both regular and bypass links. If the faults partition the network into components, such a subring will be entirely within a component. The set of faulty nodes de...