Pseudo-closure-operators
We study a particular way of introducing pseudocomplementation in ordered semigroups with zero, and characterise the class of those pseudocomplemented semigroups, termed g-semigroups here, that admit a Glivenko type theorem (the pseudocomplements form a Boolean algebra). Some further results are obtained for g-semirings - those sum-ordered partially additive semirings whose multiplicative part is a g-semigroup. In particular, we introduce the notion of a partial Stone semiring and show that several...
We study the extent to which the pseudospectra of a matrix determine other aspects of its behaviour, such as the growth of its powers and its unitary equivalence class.
The structure theory of abelian -groups does not depend on the properties of the ring of integers, in general. The substantial portion of this theory is based on the fact that a finitely generated -group is a direct sum of cyclics. Given a hereditary torsion theory on the category -Mod of unitary left -modules we can investigate torsionfree modules having the corresponding property for all torsionfree factor-modules (and a natural requirement concerning extensions of some homomorphisms). This...