A developing body of research points to the role of family relationships and interactions as factors relevant to understanding unipolar depressive symptomatology and disorder in adolescents. This paper is focused on examining mechanisms by which adverse family processes may operate to increase adolescents' vulnerability to depression. The review is organized into a description and evaluation of four potential mechanisms by which families may influence adolescents' risk: (a) Stress/Support, (b) Social Interactional, (c) Cognitive, and (d) Affect Regulation. The presentation of the individual mechanisms is followed by a brief discussion of how they could be integrated to develop a fuller understanding of familial processes relevant to the etiology and maintenance of depressive conditions. Finally, we conclude with a discussion of overall limitations in the literature and recommendations for future research.

Family processes in adolescent depression.

Preface Note to the reader Terminology, notations and conventions used List of special notation 0. Preliminaries on modules 1. Principal ideal domains 2. Firs, semifirs and the weak algorithm 3. Factorization 4. 2-firs with a distributive factor lattice 5. Modules over firs and semifirs 6. Centralizers and subalgebras 7. Skew fields of fractions Appendix Bibliography and author index Subject index.

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Free Ideal Rings and Localization in General Rings

Algebraically closed skew fields

Let Q m,n be the space of m-tuples of n × n-matrices modulo the simultaneous conjugation action of PGL n . Let Q m,n (τ) be the set of points of Q m,n of representation type τ. We show that for m ≥ n + 1 the group Aut(Q m,n ) of representation type preserving algebraic automorphisms of Q m,n acts transitively on each Q m,n (τ). Moreover, the action of Aut(Q m,n ) on the Zariski open subset Q m,n (1, n) of Q m,n is s-transitive for every positive integer s. We also prove slightly weaker analogues of these results for all m ≥ 3

On automorphisms of matrix invariants

Publisher Summary This chapter focuses on rings and algebras. The development of ring theory has been in two directions. On one hand, such instances as the quaternions and matrix algebras gave rise to the subject of linear associative algebras, which developed into the study of Artinian and Noetherian rings. On the other hand, there are the rings of algebraic integers; they are essentially Dedekind rings, which arose also in algebraic geometry as coordinate rings of curves and which formed the beginning of a very active field of study, called the commutative ring theory, which in the last few decades has had a powerful impetus from algebraic geometry. A central part of ring theory is the classification of semi-simple rings, particularly the Wedderburn theorems. There are two main approaches. The first is via semi-simple modules, possibly using homological algebra. The other is via the Jacobson structure theory, which allows the result to be derived with a minimum of assumptions.

P. M. Cohn

Papers

Progress in free associative algebras