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We study the meet irreducible ideals in certain direct limit algebras, namely the strongly maximal triangular subalgebras of AF C*-algebras. These ideals have a description in terms of the coordinates, or spectrum, that is a natural…
For a general class of non-negative functions defined on integral ideals of number fields, upper bounds are established for their average over the values of certain principal ideals that are associated to irreducible binary forms with…
A set of meet-irreducible ideals is described for a class of maximal triangular almost finite algebras. This set forms a topological space under the hull-kernel closure, and there is a one-to-one correspondence between closed sets in this…
With each Fell bundle over a discrete group G we associate a partial action of G on the spectrum of the unit fiber. We discuss the ideal structure of the corresponding full and reduced cross-sectional C*-algebras in terms of the dynamics of…
Boundary analysis is developed for a rich class of generally infinite weighted graphs with compact metric completions. These graph completions have totally disconnected boundaries. The classical notion of $\epsilon$-components and the…
We introduce a notion of integration defined from filters over families of finite sets. This procedure corresponds to determining the average value of functions whose range lies in any algebraic structure in which finite averages make…
We describe how noncommutative function algebras built from noncommutative functions in the sense of \cite{K-VV2014} may be studied as subalgebras of homogeneous $C^{*}$-algebras.
We give complete, finite quasiequational axiomatisations for algebras of unary partial functions under the operations of composition, domain, antidomain, range and intersection. This completes the extensive programme of classifying algebras…
We review our algebraic framework for linear boundary problems (concentrating on ordinary differential equations). Its starting point is an appropriate algebraization of the domain of functions, which we have named integro-differential…
We consider the behaviour of holomorphic functions on a bounded open subset of the plane, satisfying a Lipschitz condition with exponent $\alpha$, with $0<\alpha<1$, in the vicinity of an exceptional boundary point where all such functions…
We consider A-hypergeometric functions associated to normal sets in the plane. We give a classification of all point configurations for which there exists a parameter vector such that the associated hypergeometric function is algebraic. In…
The Hochschild and cyclic homology groups are computed for the algebra of `cusp' pseudodifferential operators on any compact manifold with boundary. The index functional for this algebra is interpreted as a Hochschild 1-cocycle and…
A further significant extension is presented of the infinitely large class of differential algebras of generalized functions which are the basic structures in the nonlinear algebraic theory listed under 46F30 in the AMS Mathematical Subject…
We present a new effective Nullstellensatz with bounds for the degrees which depend not only on the number of variables and on the degrees of the input polynomials but also on an additional parameter called the {\it geometric degree of the…
We apply some basic notions from combinatorial topology to establish various algebraic properties of edge ideals of graphs and more general Stanley-Reisner rings. In this way we provide new short proofs of some theorems from the literature…
All operator algebras have (not necessarily irreducible) boundary representations. A unital operator algebra has enough such boundary representations to generate its C*-envelope.
In this paper we give new upper bounds on the regularity of edge ideals whose resolutions are k-steps linear; surprisingly, the bounds are logarithmic in the number of variables. We also give various bounds for the projective dimension of…
In the present paper derivations and *-automorphisms of algebras of unbounded operators over the ring of measurable functions are investigated and it is shown that all L^0-linear derivations and L^{0}-linear *-automorphisms are inner.…
Submodular setfunctions play an important role in potential theory, and a perhaps even more important role in combinatorial optimization. The analytic line of research goes back to the work of Choquet; the combinatorial, to the work of Rado…
Border bases are a generalization of Gr\"obner bases for zero-dimensional ideals in polynomial rings. In this article, we introduce border bases for a non-commutative ring of linear differential operators, namely the rational Weyl algebra.…