Related papers: Infinitary Noetherian Constructions I. Infinite Wo…

We construct all finite irreducible modules over Lie conformal superalgebras of type W and S.

Homological algebra of modules over posets is developed, as closely parallel as possible to that of finitely generated modules over noetherian commutative rings, in the direction of finite presentations and resolutions. Centrally at issue…

We provide base change theorems, projection formulae and Verdier duality for both cohomology and homology in the context of finite topological spaces

Let $S^{\cdot}$ be a noetherian graded algebra over a commutative $k$-algebra $A$, where $k$ is a commutative ring, and assume it is a module over a Lie algebroid ${\mathfrak g}_{A/k}$. If $S^\cdot$ is semi-simple over ${\mathfrak g}_{A/k}$…

We introduce strings in metric spaces and define string complexes of metric spaces. We describe the class of 2-dimensional topological spaces which arise in this way from finite metric spaces.

Over the topos of sets, the notion of Lawvere theory is infinite countably-sorted algebraic but not one-sorted algebraic. Shifting viewpoint over the object-classifier topos, a finite algebraic presentation of Lawvere theories is…

Higher structures - infinity algebras and other objects up to homotopy, categorified algebras, `oidified' concepts, operads, higher categories, higher Lie theory, higher gauge theory... - are currently intensively investigated in…

Semigroups generated by topological operations such as closure, interior or boundary are considered. It is noted that some of these semigroups are in general finite and noncommutative. The problem is formulated whether they are always…

This short survey article reviews current understand- ing of the structure of noetherian Hopf algebras. The focus is on homological properties. A number of open problems are listed.

We give a classification theorem of certain geometric objects, called torsors over the sheaf of K-theory spaces, in terms of Tate vector bundles. This allows us to present a very natural and simple, alternative approach to the Tate central…

We consider two-variable first-order logic FO2 over infinite words. Restricting the number of nested negations defines an infinite hierarchy; its levels are often called the half-levels of the FO2 quantifier alternation hierarchy. For every…

Let R be a commutative, noetherian, local ring. Topological Q-vector spaces modelled on full subcategories of the derived category of R are constructed in order to study intersection multiplicities.

We begin the study of the consequences of the existence of certain infinite matrices. Our present application is to compactness of products of topological spaces.

We discuss various infinite-dimensional configuration spaces that carry measures quasiinvariant under compactly-supported diffeomorphisms of a manifold M corresponding to a physical space. Such measures allow the construction of unitary…

We characterize the squares occurring in infinite overlap-free binary words and construct various alpha power-free binary words containing infinitely many overlaps.

We extend the definition of conical representations for Riemannian symmetric spaces to a certain class of infinite-dimensional Riemannian symmetric spaces. Using an infinite-dimensional version of Weyl's Unitary Trick, there is a…

For a commutative ring $R$ with unit $1\ne 0$ and a multiplicatively closed subset $S$ of $R$, we introduce a new topology on the $S$-prime spectrum $\mathrm{Spec}_SR$ of $R$ called the $S$-flat topology. Our aims is to give an algebraic…

On a finite structure, the polymorphism invariant relations are exactly the primitively positively definable relations. On infinite structures, these two sets of relations are different in general. Infinitary primitively positively…

In the article at hand, we sketch how, by utilizing nilpotency to its fullest extent (Engel, Super Engel) while using methods from the theory of universal enveloping algebras, a complete description of the indecomposable representations may…

In this article we give two different ways of representations of circular words. Representations with tuples are intended as a compact notation, while representations with trees give a way to easily process all conjugates of a word. The…