Let R be a commutative noetherian ring. Denote by $${\textsf{mod }}\,R$$ the category of finitely generated R-modules. In this paper, we study n-torsionfree modules in sense Auslander and Bridger, comparing them with n-syzygy modules, satisfying Serre’s condition $$(\mathrm {S}_n)$$ . We mainly investigate closedness properties full subcategories consisting those modules.

A permutation group G?Sym(?) is said to be 2-closed if no H such that G<H?Sym(?) has the same orbits on ?×? as G. simple and efficient inductive criterion for 2-closedness established abelian groups with cyclic transitive constituents.

Based on the concept of limit of prefilters and residual implication, several notions in fuzzy topology are fuzzyfied in the sense that, for each notion, the degree to which it is fulfilled is considered. We establish therefore theories of degrees of compactness and relative compactness, of closedness, and of continuity. The resulting theory generalizes the corresponding “crisp” theory in the r...

We introduce stochastic integer programs with dominance constraints induced by mixed-integer linear recourse. Closedness of the constraint set mapping with respect to perturbations of the underlying probability measure is derived. For discrete probability measures, large-scale, block-structured, mixed-integer linear programming equivalents to the dominance constrained stochastic programs are id...

Multi-species reaction-diffusion systems, with more-than-two-site interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution equation for Ea n (t)’s, the expectation value of the product of certain linear combination of the number operators on n consecutive sites at time...

Drawing from the optimal transport theory adapted to the Lorentzian setting, we propose and study the extension of the Sorkin–Woolgar causal relation K+ onto the space of Borel probability measures on a given spacetime. We show that it retains its fundamental properties of transitivity and closedness. Furthermore, we list and prove several characterizations of this relation, including the “meas...

In this paper, we give sufficient conditions for the upper semicontinuity property of the solution mapping of a parametric generalized vector quasiequilibrium problem with mixed relations and moving cones. The main result is proven under the assumption that moving cones have local openness/local closedness properties and set-valued maps are cone-semicontinuous in a sense weaker than the usual s...

A factorization of a Galois connection investigated earlier is used to give a definition of a connectedness-disconnectedness Galois connection that is free of the notion of constant morphism. A new notion of N -fixed morphism with respect to a classN of monomorphisms is presented. This is used to characterize the connectedness-disconnectedness Galois connection in the case that N is closed unde...

• unify, and generalize seemingly disparate, classical sufficient conditions: polyhedrality of the cone, and “Slater” type conditions; • are necessary and sufficient, when the dual cone belongs to a class, that we call nice cones. Nice cones subsume all cones amenable to treatment by efficient optimization algorithms: for instance, polyhedral, semidefinite, and p-cones. • provide similarly attr...

In this note, we study how the depths of multiplier ideals behave under restriction. We also study possible values of the depths of multiplier ideals in the filtrations induced from maximal ideal sheaves. We then use it to give a sufficient condition for the integral closedness of the product of a multiplier ideal and a power of maximal ideal sheaf in the spirit of Huneke.