We define an integral domain D to be anti-Archimedean if ⋂∞ n=1 a nD 6= 0 for each 0 6= a ∈ D. For example, a valuation domain or SFT Prüfer domain is anti-Archimedean if and only if it has no height-one prime ideals. A number of constructions and stability results for anti-Archimedean domains are given. We show that D is anti-Archimedean ⇔ D[[X1, . . .

In this paper we present O(n)-time algorithms for encoding/decoding n-node labeled trees as sequences of n−2 node labels. All known encodings of this type are covered, including Prüfer-like codes and the three codes proposed by Picciotto the happy, blob, and dandelion codes. The algorithms for Picciotto’s codes are of special significance as previous publications describe suboptimal approaches ...

We show that every tilting module of projective dimension one over a ring R is associated in a natural way to the universal localization R → RU at a set U of finitely presented modules of projective dimension one. We then investigate tilting modules of the form RU ⊕ RU/R. Furthermore, we discuss the relationship between universal localization and the localization R → QG given by a perfect Gabri...