Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

This text, drawn from the author's lectures at the University of California at Berkeley, is intended as a textbook for a one-term course in basic ring theory. The material covered includes the Wedderburn-Artin theory of semi-simple rings, Jacobson's theory of the radical representation theory of groups and algebras, prime and semi-prime rings, primitive and semi-primitive rings, division rings, ordered rings, local and semi-local rings, and perfect and semi-perfect rings. By aiming the level of writing at the novice rather than at the expert, and by stressing the role of examples and motivation, the author has produced a text which is suitable not only for use in a graduate course, but also for self-study by other interested graduate students. Numerous exercises are also included. This graduate textbook on rings, fields and algebras is intended for graduate students in mathematics.

A first course in noncommutative rings, by T. Y. Lam. Pp. 385. £37 (pb), £62.50 (hb). 2001. ISBN 0 387 95325 6 (pb), 0 387 95183 0 (hb) (Springer-Verlag).

© Publications mathématiques de l’I.H.É.S., 1988, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http:// www.ihes.fr/IHES/Publications/Publications.html) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

Semianalytic and subanalytic sets . The deformation theory of representations of fundamental groups of compact Kähler manifolds . Canonical models of surfaces of general type in positive characteristic . Cuspidal local systems and graded Hecke algebras, I

Model‐Theoretic Algebra With particular emphasis on fields, rings, modules

We define the Grothendieck group of an n-exangulated category. For n odd, we show that this group shares many properties with the Grothendieck group of an exact or a triangulated category. In particular, we classify dense complete subcategories of an n-exangulated category with an n-(co)generator in terms of subgroups of the Grothendieck group. This unifies and extends results of Thomason, Bergh–Thaule, Matsui and Zhu–Zhuang for triangulated, $$(n+2)$$
 -angulated, exact and extriangulated categories, respectively. We also introduce the notion of an n-exangulated subcategory and prove that the subcategories in our classification theorem carry this structure.

The Grothendieck Group of an n -exangulated Category

Transport of structure in higher homological algebra

In this thesis we introduce a class of semiperfect rings which generalise the class of
finite-dimensional gentle algebras. We consider complexes of modules over these rings
which have finitely generated projective homogeneous components. We then classify them
up to homotopy equivalence. The method we use to solve this classification problem is
called the functorial filtrations method. The said method was previously only used to
classify modules.

Functorial Filtrations for Semiperfect generalisations of Gentle Algebras

. Additive categories play a fundamental role in mathematics and related discip-lines. Given an additive category equipped with a biadditive functor, one can construct its category of extensions, which encodes important structural information. We study how functors between categories of extensions relate to those at the level of the original categories. When the additive categories in question are n -exangulated, this leads to a characterisation of n -exangulated functors. Our approach enables us to study n -exangulated categories from a 2 -categorical perspective. We introduce n -exangulated natural transformations and characterise them using categories of extensions. Our characterisations allow us to establish a 2 -functor between the 2 -categories of small n -exangulated categories and small exact categories. A similar result with no smallness assumption is also proved. We employ our theory to produce various examples of n -exangulated functors and natural transformations. Although the motivation for this article stems from representation theory and the study of n -exangulated categories, our results are widely applicable: several require only an additive category equipped with a biadditive functor with no extra assumptions; others can be applied by endowing an additive category with its split n -exangulated structure.

The category of extensions and a characterisation of $n$-exangulated functors

We consider algebras defined over a complete, local and noetherian ground ring. They are gentle algebras in case the ground ring is a field. The unbounded homotopy category of complexes of projective modules is considered. Complexes with finitely-generated homogeneous components are shown to be isomorphic to direct sums of indecomposable string and band complexes. The corresponding isoclasses are described, and the Krull-Remak-Schmidt-Azumaya property is verified. This classification problem is solved using the idea of functorial filtrations.

Functorial filtrations for homotopy categories of some generalisations of gentle algebras

We prove that indecomposable $\Sigma$-pure-injective modules for a string algebra are string or band modules The key step in our proof is a splitting result for infinite-dimensional linear relations

Raphael Bennett-Tennenhaus

Papers

Transport of structure in higher homological algebra

Functorial Filtrations for Semiperfect generalisations of Gentle Algebras

The category of extensions and a characterisation of $n$-exangulated functors

Functorial filtrations for homotopy categories of some generalisations of gentle algebras

$\Sigma$-pure-injective modules for string algebras and linear relations