We define the spectrum of a tensor triangulated category K as the set of so-called prime ideals, endowed with a suitable topology. In this very generality, the spectrum is the universal space in which one can define supports for objects of K. This construction is functorial with respect to all tensor triangulated functors. Several elementary properties of schemes hold for such spaces, e.g. the ...

The prime spectra of two families of algebras, Sw and Šw, w ∈ W, indexed by the Weyl group W of a semisimple finitely dimensional Lie algebra g, are studied in the spirit of [J3]. The algebras Sw have been introduced by A. Joseph (see [J4], Sect. 3). They are q-analogues of the algebras of regular functions on w-translates of the open Bruhat cell of a semisimple Lie group G corresponding to the...

We study prime algebras of quadratic growth. Our first result is that if A is a prime monomial algebra of quadratic growth then A has finitely many prime ideals P such that A/P has GK dimension one. This shows that prime monomial algebras of quadratic growth have bounded matrix images. We next show that a prime graded algebra of quadratic growth has the property that the intersection of the non...

Article history: Received 28 June 2012 Revised 2 December 2012 Accepted 10 January 2013 Available online 31 January 2013 Communicated by Gary McGuire

This paper is a companion to the Boardman–Wilson paper on the ring spectrum P (n). When the prime is 2, this spectrum is not commutative, which introduces several complications. Here, we supply the necessary details of the relevant Hopf algebroids and Hopf ring for this case.

Scott’s information systems provide a categorically equivalent, intensional description of Scott domains and continuous functions. Following a well established pattern in denotational semantics, we define a linear version of information systems, providing a model of intuitionistic linear logic (a newSeely category), with a “set-theoretic” interpretation of exponentials that recovers Scott conti...

Denote by λ(n) Liouville’s function concerning the parity of the number of prime divisors of n. Using a theorem of Allouche, Mendès France, and Peyrière and many classical results from the theory of the distribution of prime numbers, we prove that λ(n) is not k–automatic for any k > 2. This yields that P ∞ n=1 λ(n)X ∈ Fp[[X]] is transcendental over Fp(X) for any prime p > 2. Similar results are...

In this paper we attempt to find and investigate the most general class of posets which satisfy a properly generalized version of the Hofmann-Mislove theorem. For that purpose, we generalize and study some notions (like compactness, the Scott topology, Scott open filters, prime elements, the spectrum etc.), and adjust them for use in general posets instead of frames. Then we characterize the po...

We present an algorithm to find lower bounds for multicolor classical Ramsey numbers by using 2-normalized cyclic graphs of prime order, and use it to obtain new lower bounds for two multicolor classical Ramsey numbers: R(3, 3, 12) ≥ 182, R(3, 3, 13) ≥ 212.

Inspired by the classical concept of height of a prime ideal in a ring, we proposed in a precedent paper the notion of height of a prime hyperideal in a Krasner hyperring. In this note we first generalize some results concerning the height of a prime hyperideal in a Noetherian Krasner hyperring, with the intent to extend this definition to the case of a general hyperideal in a such hyperring. T...