The statements of Main Theorem 1.1 and Theorem 2.1 of the author's paper [Trans. Amer. are affected similarly.) These restrictions can be removed if the conclusions of the results are weakened to allow for the possible existence of transitive, proper subgroups of G. In this form, the results can be extended to the setting where G is a product of real and p-adic Lie groups. There are two errors ...

Classically, a Tychonoff space is called strongly 0-dimensional if its Stone-Čech compactification is 0-dimensional, and given the familiar relationship between spaces and frames it is then natural to call a completely regular frame strongly 0-dimensional if its compact completely regular coreflection is 0-dimensional (meaning: is generated by its complemented elements). Indeed, it is then seen...

We define a quasi–projective reduction of a complex algebraic variety X to be a regular map from X to a quasi–projective variety that is universal with respect to regular maps from X to quasi–projective varieties. A toric quasi–projective reduction is the analogous notion in the category of toric varieties. For a given toric variety X we first construct a toric quasi–projective reduction. Then ...

Let A be a Koszul Artin-Schelter regular algebra, σ graded automorphism of and δ degree-one -derivation . We introduce an invariant for called the -divergence describe Nakayama Ore extension B = [ z ; , ] explicitly using construct twisted superpotential ω ˆ so that it is derivation quotient algebra defined by also determine all extensions noetherian algebras dimension 2 compute their automorph...

This paper presents some features of the Vaucanson platform. We describe some original algorithms on weighted automata and transducers (computation of the quotient, conversion of a regular expression into a weighted automaton, and composition). We explain how complex declarations due to the generic programming are masked from the user and finally we present a proposal for an XML format that all...

Let X be a completely regular space and let A(X) be a ring of continuous real-valued functions onX which is closed under local bounded inversion. We show that the structure space of A(X) is homeomorphic to a quotient of the Stone–Čech compactification of X. We use this result to show that any realcompactification of X is homeomorphic to a subspace of the structure space of some ring of continuo...

We study the computational power of pure insertion grammars. We show that pure insertion grammars of weight 3 can characterize all recursively enumerable languages. This is achieved by either applying an inverse morphism and a weak coding, or a left (right) quotient with a regular language. A consequences for the closure properties of insertion grammars are shown. We also study an application i...

In this paper, we ask the following question: what is the minimal value of the difference e HK (I) − e HK (I ′) for ideals I ′ ⊇ I with l A (I ′ /I) = 1? In order to answer to this question, we define the notion of minimal Hilbert-Kunz multiplicity for strongly F-regular rings. Moreover, we calculate this invariant for quotient singularities and for the coordinate ring of the Segre embedding: P...

In this paper, we examine the structure of vertexand edge-transitive strongly regular graphs, using normal quotient reduction. We show that the irreducible graphs in this family have quasiprimitive automorphism groups, and prove (using the Classification of Finite Simple Groups) that no graph in this family has a holomorphic simple automorphism group. We also find some constraints on the parame...