Essentially Shared Obligations

Essentially Shared Obligations

The Lake: Alice, Bertha, and Claudia live around Forest Lake, at some distance from each other. The ecosystem is sensitive, in particular to the solvent they have been using when painting their boats, and the lake is faring badly. Until recently, they had no way of knowing that the solvent would have this effect, but they just learned that it is in fact killing the fish in the lake, and that th...

Essentially Retractable Modules

We call a module  essentially retractable if HomR for all essential submodules N of M. For a right FBN ring R, it is shown that: (i)  A non-zero module  is retractable (in the sense that HomR for all non-zero ) if and only if certain factor modules of M are essentially retractable nonsingular modules over R modulo their annihilators. (ii)  A non-zero module  is essentially retractable if and on...

Co-national Obligations & Cosmopolitan Obligations towards Foreigners

On Obligations

Access control is concerned with granting access to sensitive data based on conditions that relate to the past or present, so-called provisions. Expressing requirements from the domain of data protection necessitates extending this notion with conditions that relate to the future. Obligations, in this sense, are concerned with commitments of the involved parties. At the moment of granting acces...

Essentially normal operators

This is a survey of essentially normal operators and related developments. There is an overview of Weyl–von Neumann theorems about expressing normal operators as diagonal plus compact operators. Then we consider the Brown–Douglas–Fillmore theorem classifying essentially normal operators. Finally we discuss almost commuting matrices, and how they were used to obtain two other proofs of the BDF t...