Classification of finite dimensional uniserial representations of conformal Galilei algebras

With the aid of the $6j$-symbol, we classify all uniserial modules of $\mathfrak{sl}(2)\ltimes \mathfrak{h}_{n}$, where $\mathfrak{h}_{n}$ is the Heisenberg Lie algebra of dimension $2n+1$.Comment: Some references added, introduction expanded, title change

Serial group rings of finite groups. General linear and close groups

For a given p, we determine when the p-modular group ring of a group from GL(n,q), SL(n,q) and PSL(n,q)-series is serial

Serial group rings of finite groups. General linear and close groups

For a givenp, we determine when thepmodulargroup ring of a group from GL(n,q), SL(n,q) and PSL(n,q)-seriesis serial

Serial group rings of finite groups. p-solvability

We prove that for any finite p-solvable group G with a cyclic p-Sylow subgroup and any field F of characteristic p, the group ring FG is serial. As a corollary for an arbitrary field we will produce a list of all groups of order ≤ 100 whose group rings are serial

ПРИМЕР КОЛЬЦА ЭНДОМОРФИЗМОВ ПОЛУЦЕПНОГО МОДУЛЯ

We construct an example of a serial module, whose endomorphism ring modulo by its Jacobson radical is neither von Neumann regular nor one-sided self-injective. This solves a problem posed by Alberto Facchini.Хорошо известно, что фактор кольца эндоморфизмов инъективного модуля по его радикалу Джекобсона является регулярным по Нейману самоинъективным с одной стороны кольцом. А. Факкини спросил, верно ли это для полуцепных модулей бесконечной размерности Голди. В этой статье мы построим пример, показывающий, что ответ на этот вопрос отрицательный

Serial Rings

This book presents an exhaustive and up-to-date overview of the structure theory of serial rings, and the various methods of treating them. Results have been scattered throughout the literature, and the achievements of some schools, such as the Kiev school, seem little-known. This volume endeavours to unify the wide spectrum of tools used in this area and state the theory of serial rings based on two constructions: firstly, localisation with respect to a semi-prime Goldie ideal; and, secondly, a hidden 'blow-up' construction in a serial ring. Part of the work deals with the theory of modules over a serial ring, especially with finitely presented and pure injective modules. Other topics include noetherian serial rings and Artinian serial rings. Audience: This volume can be used as a textbook in ring theory and in the model theory of modules, and will also be of interest to postgraduates and researchers whose work involves rings and algebras

Decidability of modules over a Bézout domain D+XQ[X] with D a principal ideal domain and Q its field of fractions

We describe the Ziegler spectrum of a Bézout domain B = D+XQ[X] where D is a principal ideal domain and Q is its field of fractions, in particular we ccompute the Cantor-Bendixson rank of the space. Using this, we prove the decidability of the theory of B-modules when D is "sufficiently" recursive

Superdecomposable pure-injective modules and integral group rings

We prove that, if G is a non-trivial finite group, then the integral group ring ZG possesses a superdecomposable pure-injective module