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Infinite Abelian groups

01 Jan 1970-
About: The article was published on 1970-01-01 and is currently open access. It has received 2613 citations till now. The article focuses on the topics: Elementary abelian group & Rank of an abelian group.
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Book
01 Jan 1999
TL;DR: In this article, the authors introduce surfaces in 4-manifolds complex surfaces and Kirby calculus, a calculus based on handelbodies and Kirby diagrams, which is used for handel bodies and kirby diagrams.
Abstract: 4-manifolds: Introduction Surfaces in 4-manifolds Complex surfaces Kirby calculus: Handelbodies and Kirby diagrams Kirby calculus More examples Applications: Branched covers and resolutions Elliptic and Lefschetz fibrations Cobordisms, $h$-cobordisms and exotic ${\mathbb{R}}^{4,}$s Symplectic 4-manifolds Stein surfaces Appendices: Solutions Notation, important figures Bibliography Index.

1,412 citations

Reference BookDOI
11 May 2018
TL;DR: In this paper, a comprehensive introduction to module theory and the related part of ring theory, including original results as well as the most recent work, is presented and accompanied by complete proofs, where the smallest Grothendieck category containing it is denoted by o[M] and module theory is developed in this category.
Abstract: This volume provides a comprehensive introduction to module theory and the related part of ring theory, including original results as well as the most recent work. It is a useful and stimulating study for those new to the subject as well as for researchers and serves as a reference volume. Starting form a basic understanding of linear algebra, the theory is presented and accompanied by complete proofs. For a module M, the smallest Grothendieck category containing it is denoted by o[M] and module theory is developed in this category. Developing the techniques in o[M] is no more complicated than in full module categories and the higher generality yields significant advantages: for example, module theory may be developed for rings without units and also for non-associative rings. Numerous exercises are included in this volume to give further insight into the topics covered and to draw attention to related results in the literature.

1,141 citations

DOI
01 Jan 1970

670 citations

Book
01 Jan 1998
TL;DR: In this paper, the authors give a complete presentation of the theory of proper forcing and its relatives, starting from the beginning and avoiding the metamathematical considerations, and show methods which can be used for such independence results.
Abstract: This work deals with set-theoretic independence results (independence from the usual set-theoretic ZFC axioms), in particular for problems on the continuum. Consequently, the theory of iterated forcing is developed. The author gives a complete presentation of the theory of proper forcing and its relatives, starting from the beginning and avoiding the metamathematical considerations. In addition to particular consistency results, the author shows methods which can be used for such independence results. Many of these are presented in an "axiomatic" framework (a la Martin's axiom) for this reason. The main aim of this book is to enable a researcher interested in an independence result of the appropriate kind, to have much of the work done for him, thus allowing him to quote general results.

556 citations

MonographDOI
01 Jan 1988

339 citations