849 research outputs found
Relational type-checking for MELL proof-structures. Part 1: Multiplicatives
Relational semantics for linear logic is a form of non-idempotent
intersection type system, from which several informations on the execution of a
proof-structure can be recovered. An element of the relational interpretation
of a proof-structure R with conclusion acts thus as a type (refining
) having R as an inhabitant. We are interested in the following
type-checking question: given a proof-structure R, a list of formulae ,
and a point x in the relational interpretation of , is x in the
interpretation of R? This question is decidable. We present here an algorithm
that decides it in time linear in the size of R, if R is a proof-structure in
the multiplicative fragment of linear logic. This algorithm can be extended to
larger fragments of multiplicative-exponential linear logic containing
-calculus
Glueability of Resource Proof-Structures: Inverting the Taylor Expansion
A Multiplicative-Exponential Linear Logic (MELL) proof-structure can be expanded into a set of resource proof-structures: its Taylor expansion. We introduce a new criterion characterizing those sets of resource proof-structures that are part of the Taylor expansion of some MELL proof-structure, through a rewriting system acting both on resource and MELL proof-structures
Directed unions of local quadratic transforms of regular local rings and pullbacks
Let be an infinite sequence of regular
local rings with birationally dominating and a principal ideal of for each . We examine properties
of the integrally closed local domain .Comment: 23 pages; comments welcom
Mapping resolutions of length three I
We produce some interesting families of resolutions of length three by
describing certain open subsets of the spectrum of the generic ring for such
resolutions constructed in a recent paper by Weyman.Comment: 23 page
Asymptotic invariants of ideals with Noetherian symbolic Rees algebra and applications to cover ideals
Let be an ideal whose symbolic Rees algebra is Noetherian. For , the -th symbolic defect, sdefect, of is defined to be the
minimal number of generators of the module . We prove that
sdefect is eventually quasi-polynomial as a function in . We compute
the symbolic defect explicitly for certain monomial ideals arising from graphs,
termed cover ideals. We go on to give a formula for the Waldschmidt constant,
an asymptotic invariant measuring the growth of the degrees of generators of
symbolic powers, for ideals whose symbolic Rees algebra is Noetherian.Comment: 22 pages, 5 figure
Mapping free resolutions of length three II -- Module formats
Let be a perfect module of projective dimension 3 in a Gorenstein, local
or graded ring . We denote by \FF the minimal free resolution of .
Using the generic ring associated to the format of \FF we define higher
structure maps, according to the theory developed by Weyman in "Generic free
resolutions and root systems" (Annales de l'Institut Fourier} 68.3 (2018), pp.
1241--1296). We introduce a generalization of classical linkage for -module
using the Buchsbaum--Rim complex, and study the behaviour of structure maps
under this Buchsbaum--Rim linkage. In particular, for certain formats we obtain
criteria for these -modules to lie in the Buchsbaum--Rim linkage class of a
Buchsbaum--Rim complex of length 3.Comment: 30 page
On the integral domains characterized by a Bezout Property on intersections of principal ideals
In this article we study two classes of integral domains. The first is
characterized by having a finite intersection of principal ideals being
finitely generated only when it is principal. The second class consists of the
integral domains in which a finite intersection of principal ideals is always
non-finitely generated except in the case of containment of one of the
principal ideals in all the others. We relate these classes to many
well-studied classes of integral domains, to star operations and to classical
and new ring constructions.Comment: 22 page
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