we define and studyco-noetherian dimension of rings for which the injective envelopeof simple modules have finite krull-dimension. this  is a moritainvariant dimension that measures how far the ring is from beingco-noetherian. the co-noetherian dimension of certain rings,including commutative rings, are determined. it is shown that the class ${mathcal w}_n$ of rings with co-noetherian dimension...

An intersection type assignment system for the extension ΛJ of the untyped λ-calculus, introduced by Joachimski and Matthes, is given and proven to characterize the strongly normalizing terms of ΛJ. Since ΛJ’s generalized applications naturally allow permutative/commuting conversions, this is the first analysis of a term rewrite system with permutative conversions by help of intersection types....

 In this paper, a new homological dimension of modules, copresented dimension, is defined. We study some basic properties of this homological dimension. Some ring extensions are considered, too. For instance, we prove that if $Sgeq R$ is a finite normalizing extension and $S_R$ is a projective module, then for each right $S$-module $M_S$, the copresented dimension of $M_S$ does not exceed the c...

We characterize sets of strings using two central properties from rewriting: normalization and termination. We recall the well-known result that any recursively enumerable set of strings can occur as the set of normalizing strings over a “small” alphabet if the rewriting system is allowed access to a “larger” alphabet (and extend the result to termination). We then show that these results do no...

We characterize sets of strings using two central properties from rewriting: normalization and termination. We recall the well-known result that any recursively enumerable set of strings can occur as the set of normalizing strings over a “small” alphabet if the rewriting system is allowed access to a “larger” alphabet (and extend the result to termination). We then show that these results do no...

Several systems of xed-point types (also called retract types or recursive types with explicit isomorphisms) extending system F are considered. The seemingly strongest systems have monotonicity witnesses and use them in the deenition of beta reduction for those types. A more na ve approach leads to non-normalizing terms. All the other systems are strongly normalizing because they embed in a red...

Inductive characterizations of the sets of terms, the subset of strongly normalizing terms and normal forms are studied in order to reprove weak and strong normalization for the simplytyped λ-calculus and for an extension by sum types with permutative conversions. The analogous treatment of a new system with generalized applications inspired by generalized elimination rules in natural deduction...

We define a differential λμ-calculus which is an extension of both Parigot’s λμ-calculus and EhrhardRégnier’s differential λ-calculus. We prove some basic properties of the system: reduction enjoys ChurchRosser and simply typed terms are strongly normalizing.

We present a method of lifting to explicit substitution calculi some characterizations of the strongly normalizing terms of λ-calculus by means of intersection type systems. The method is first illustrated by applying to a composition-free calculus of explicit substitutions, yielding a simpler proof than the previous one by Lengrand et al. Then we present a new intersection type system in the s...

We present a sequent calculus that allows to abstract over a type variable. The introduction of the abstraction on the right-hand side of a sequent corresponds to the universal quantification; whereas, the introduction of the abstraction on the lefthand side of a sequent corresponds to the existential quantification. The calculus provides a correspondence with second-order classical proposition...