On ω-Linked Overrings

Let R (C) T be an extension of commutative rings. T is called ω-linked over R if T as an R-module is a ω-module. In the case of R (C) T (C) Q0(R), T is called a ω-linked overring of R. As a generalization of Wang-McCsland-Park-Chang Theorem, we show that if R is a reduced ring, then R is a ω-Noetherian ring with ω-dim(R) ≤1 if and only if each ω-linked overring T of R is a ω-Noetherian ring with ω-dim(T) ≤ 1. In particular, R is a ω-Noetherian ring with ω-dim(R) = 0 if and only if R is an Artinian ring.     

On U-ample ω-semigroups

The investigation of U-ample ω-semigroups is initiated. After obtaining some properties of such semigroups, a structure of U-ample ω-semigroups is established. It is proved that a semigroup is a U-ample ω-semigroup if and only if it can be expressed by WBR（T, 0）, namely, the weakly Bruck-Reilly extensions of a monoid T. This result not only extends and amplifies the structure theorem of bisimple inverse ω-semigroups given by N. R. Reilly, but also generalizes the structure theorem of ,-bisimple type A ω-semigroups given by U. Asibong-Ibe in 1985.     

Cut-elimination for ω1

In this paper we calibrate the strength of the soundness of a set theory $\mathsf{KP}\omega +({\mathrm{\Pi }}_1\text{-Collection})$ with the assumption that ‘there exists an uncountable regular ordinal’ in terms of the existence of ordinals.     

On ω-Categorical Theory

In[1],forn-typesofthefirstordertheoryT,astonespaceofn-typesisestablished.Usingtheaboveideainananalogousway,wemayconstructatopologicalspaceofn-types.Withoutlossofgenerality,weonlydiscuss-types.LetTbeacompletetheoryinacountablelanguageL-LetS1(T)={p:pis...     

A convergent simplicial algorithm with ω-subdivision and ω-bisection strategies

The simplicial algorithm is a kind of branch-and-bound method for computing a globally optimal solution of a convex maximization problem. Its convergence under the ω-subdivision strategy was an open question for some decades until Locatelli and Raber proved it (J Optim Theory Appl 107:69–79, 2000). In this paper, we modify their linear programming relaxation and give a different and simpler proof of the convergence. We also develop a new convergent subdivision strategy, and report numerical results of comparing it with existing strategies.     

Variations on ω-boundedness

Let be a property (or, equivalently, a class) of topological spaces. A space X is called -bounded if every subspace of X with (or in) has compact closure. Thus, countable-bounded has been known as ω-bounded and (σ-compact)-bounded as strongly ω-bounded. In this paper we present a systematic study of the interrelations of these two known “boundedness” concepts with -boundedness where is one of the further countability properties weakly Lindelöf, Lindelöf, hereditarily Lindelöf, and ccc.     

Some ω-unique and ω-P Properties for Linear Transformations on Hilbert Spaces

Given a real （finite-dimensional or infinite-dimensional） Hilbert space H with a Jordan product, we introduce the concepts of ω-unique and ω-P properties for linear transformations on H, and investigate some interconnections among these concepts. In particular, we discuss the ω-unique and ω-P properties for Lyapunov-like transformations on H. The properties of the Jordan product and the Lorentz cone in the Hilbert space play important roles in our analysis.     

Square of ω-hyponormal operators

In this paper, we show that ifT is a -hyponormal operator, thenT ² is also -hyponormal.     

Regular Bisimple ω2-semigroups

The regular semigroups S with an idempotent set Es = {e0,e1,…,en,…} such that e0 ＞ e1 ＞…＞ en ＞… is called a regular ω-semigroup. In [5] Reilly determined the structure of a regular bisimple ω-semigroup as BR(G,θ),which is the classical Bruck-Reilly extension of a group G.     

Nice Enumerations of ω-categorical Groups

We give an example of an ω-categorical group without AZ-enumerations. We build AZ-enumerations of some ω-categorical central products of ω copies of a finite 2-step nilpotent group.     

Compact spaces of Szlenk index ω

The Szlenk index has found many applications in the isomorphic theory of Banach spaces. Its definition is based in some kind of interplay between a weak topology and the norm metric with not much care on the linear structure. There is no obstacle to consider the notion of Szlenk index in more general settings. In this paper we study the compact spaces of Szlenk index ω at most with respect to an associated metric. We include new applications to Banach spaces of the these methods, where the estimations of the growth speed of the finite Szlenk indices play a fundamental role.     

An ω-hierarchy of axiom systemZF

In this paper we develop a sequenceZ ₀,...,Z _n ,...(n) of axiom systems for set theory, such that (1) the consistency of any system within the sequence is provable in its succeeding systems, (2) the first system in the sequence is Zermelo 's systemZ and the union of all systems in the sequence is justZF.     

Orientals as free weak ω-categories

The orientals are the free strict ω-categories on the simplices introduced by Street. The aim of this paper is to show that they are also the free weak ω-categories on the same generating data. More precisely, we exhibit the complicial nerves of the orientals as fibrant replacements of the simplices in Verity's model structure for weak complicial sets.     

The global dimension of ω-smash coproducts

We mainly study the global dimension of ω-smash coproducts. We show that if H is a Hopf algebra with a bijective antipode S _H , and C _ω ? H denotes the ω-smash coproduct, then gl.dim(C _ω ? H) ≤ gl.dim(C) + gl.dim(H), where gl.dim(H) denotes the global dimension of H as a coalgebra.     

Some local properties of ω-stable groups

In this note we study some local properties of-stable groups of finite Morley rank.     

Some topological properties of ω-covering sets

We prove the following theorems:1. There exists an -covering with the property s ₀.2. Under cov there exists X such that is not an -covering orX \ B is not an -covering].3. Also we characterize the property of being an -covering.     

Minimal Hereditary ω-Local Non-ℌ-Formations

We describe minimal hereditary -local non--formations, where is a formation of the classical type.     

Bending of point correspondences. ω-systems

Apart from the literature we investigate special systems of quadratic forms (-systems) that have significance in the theory of bending of point correspondences.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 16, pp. 3–34, 1984.