Grigore Calugareanu - Böcker

This text contains almost 350 exercises in basic ring theory, with the solutions given in as much detail as possible. Subjects treated include zero divisors, ring homomorphisms, divisibility in integral domains, division rings, automorphisms, the tensor product, artinian and noetherian rings, socle and radical rings, semisimple rings, polynomial rings, rings of quotients, and rings of continuous functions. This volume is recommended for lecturers and graduate students involved in associative rings and algebras, commutative rings and algebras, algebraic number theory, field theory and polynomials, order, lattices, and general topology.

This volume is dedicated to the use of lattice theory in module theory. Its main purpose is to present all module-theoretic results that can be proved by lattice theory only, and to develop the theory necessary to do so. The results treated fall into categories such as the origins of lattice theory, module-theoretic results generalized in modular and likely compactly generated lattices, very special module-theoretic results generalized in lattices, and new concepts in lattices introduced by the author.

This work on Abelian Group Theory (or Group Theory) to cover elementary results in Abelian Groups. It contains comprehensive coverage of almost all the topics related to the theory and is designed to be used as a course book for students at both undergraduate and graduate level. The text caters to students of differing capabilities by categorising the exercises in each chapter according to their level of difficulty starting with simples exercises (marked S1, S2 etc), medium difficulty (M1, M2 etc) and ending with the difficult exercises (D1, D2 etc). Solutions for all of the exercises are included. This book should also appeal to experts in the field as an excellent reference to a large number of examples in Group Theory.

This book contains almost 350 exercises in basic ring theory. The problems form the 'folklore' of ring theory, and the solutions are given in as much detail as possible. This makes the work ideally suited for self-study. Subjects treated include zero divisors, ring homomorphisms, divisibility in integral domains, division rings, automorphisms, the tensor product, artinian and noetherian rings, socle and radical rings, semisimple rings, polynomial rings, rings of quotients, and rings of continuous functions. Audience: This volume is recommended for lecturers and graduate students involved in associative rings and algebras, commutative rings and algebras, algebraic number theory, field theory and polynomials, order, lattices, and general topology.

This volume is dedicated to the use of lattice theory in module theory. Its main purpose is to present all module-theoretic results that can be proved by lattice theory only, and to develop the theory necessary to do so. The results treated fall into categories such as the origins of lattice theory, module-theoretic results generalised in modular and likely compactly generated lattices, very special module-theoretic results generalised in lattices, and new concepts in lattices introduced by the author. Audience: This book will be of interest to graduate students and researchers whose work involves order, lattices, group theory and generalisations, general module theory, and rings and algebras.