relative to a hereditary torsion theory $tau$ we introduce a dimension for a module $m$, called {em $tau$-rank of} $m$, which coincides with the reduced rank of $m$ whenever $tau$ is the goldie torsion theory. it is shown that the $tau$-rank of $m$ is measured by the length of certain decompositions of the $tau$-injective hull of $m$. moreover, some relations between the $tau$-rank of $m$ and c...

The Yang-Baxter equation plays a fundamental role in various areas of mathematics. Its solutions, called braidings, are built, among others, from Yetter-Drinfeld modules over a Hopf algebra, from self-distributive structures, and from crossed modules of groups. In the present paper these three sources of solutions are unified inside the framework of Yetter-Drinfeld modules over a braided system...

This paper proposes a compositional model-theoretic account of the way the interpretation of indicative conditionals is determined and constrained by the temporal and modal expressions in their constituents. The main claim is that the tenses in both the antecedent and the consequent of an indicative conditional are interpreted in the same way as in isolation. This is controversial for the antec...

PREFACE 1022 CHAPTER I. The sources of errors in a computation 1.1. The sources of errors. (A) Approximations implied by the mathematical model. (B) Errors in observational data. (C) Finitistic approximations to transcendental and implicit mathematical formulations. (D) Errors of computing instruments in carrying out elementary operations: "Noise." Round off errors. "Analogy" and digital comput...

links the clauses “you need anything” and “I’m Jill” in a conditional construction, but semantically we may naturally perceive the propositions expressed by these clauses as conditionally unrelated; the name of the woman does not depend on whether the addressee needs anything or not. To humorously misapprehend such conditional sentences, as Martin does, is to pretend to see a conditional relati...