This expository monograph was written for three reasons. Firstly, we wanted to present the
solution to a problem posed by Wolfgang Krull in 1932 [Krull 32]. He asked whether what we …

Let R be an associative ring. This monograph deals with the right R-modules MR whose
endomorphism ring End (MR) is semilocal. More generally, let A be any preadditive …

Commutative rings all of whose quotients over non-zero ideals are perfect rings are called
almost perfect. Revisiting a paper by JR Smith on local domains with TTN, some basic …

References Page 1 References [1] FW Anderson and KR Fuller, Rings and Categories of
Modules, SpringerVerlag, New York (1974). [2] VI Arnautov, ST Glavatsky, and AV Mikhalev …

We study the maximal immediate extensions of valued fields whose residue fields are
perfect and whose value groups are divisible by the residue characteristic if it is positive. In …

We construct a noncommutative desingularization of the discriminant of a finite reflection
group G as a quotient of the skew group ring A= S∗ G. If G is generated by order 2 …

Discrete valuation domains form a class of local domains close to division rings. However, it
follows from our definition that a division ring is not a discrete valuation domain. A discrete …

The discussion of almost perfect domains and their modules presented in this survey paper
is divided in two parts. In the first part the ring-theoretical properties of almost perfect …

Chemometric data evaluation methods for time‐of‐flight secondary ion mass spectrometry
(TOF‐SIMS) have been tested for the characterization and classification of minerals …

For a discrete valuation ring R, let ${\text {fr}}(R) $ be the supremum of the ranks of
indecomposable finite rank torsion-free R-modules. Then ${\text {fr}}(R)= 1, 2, 3$, or $\infty …