Given an adjoint pair of functors F,G, the composite GF naturally gets the structure of a monad. The same monad may arise from many such adjoint pairs of functors, however. Can one describe all of the adjunctions giving rise to a given monad? In this paper we single out a class of adjunctions with especially good properties, and we develop methods for computing all such adjunctions, up to natur...

First, we give a complete description of the indecomposable prime modules over a Dedekind domain. Second, if R is the pullback, in the sense of [9], of two local Dedekind domains then we classify indecomposable prime R-modules and establish a connection between the prime modules and the pure-injective modules (also representable modules) over such rings.

We prove a new structural result for the spherical Tits building attached to GLnK for many number fields K, and more generally for the fraction fields of many Dedekind domains O: the Steinberg module Stn(K) is generated by integral apartments if and only if the ideal class group cl(O) is trivial. We deduce this integrality by proving that the complex of partial bases of O is Cohen–Macaulay. We ...

Abstract Let R be a ring and let M an -module with $$S={\text {End}}_R(M)$$ S = End R ( M ) . The module is called quasi-dual Baer if for every fully invari...

We introduce the $h$-adic quantum vertex algebras associated with trigonometric $R$-matrices in types $B$, $C$ and $D$, thus generalizing well-known Etingof-Kazhdan construction type $A$. show that restricted modules for affine $D$ are naturally equipped structure of $\phi$-coordinated module aforementioned algebras.

In the absence of the axiom of choice there are several possible nonequivalent ways of translating the intuitive idea of “infinity” into a mathematical definition. In [10], Tarski investigated some natural infinity notions notions, and his research was continued by Levy [8], Truss [12], Spǐsiak and Vojtas [9], Howard and Yorke [4] and others. The most prominent definitions of finiteness are the...

Tits has defined Steinberg groups and Kac-Moody groups for any root system and any commutative ring R. We establish a Curtis-Tits-style presentation for the Steinberg group St of any rank ≥ 3 irreducible affine root system, for any R. Namely, St is the direct limit of the Steinberg groups coming from the 1and 2-node subdiagrams of the Dynkin diagram. This leads to a completely explicit presenta...