## Module Theory, Extending Modules and GeneralizationsThe main focus of this monograph is to offer a comprehensive presentation of known and new results on various generalizations of CS-modules and CS-rings. Extending (or CS) modules are generalizations of injective (and also semisimple or uniform) modules. While the theory of CS-modules is well documented in monographs and textbooks, results on generalized forms of the CS property as well as dual notions are far less present in the literature. With their work the authors provide a solid background to module theory, accessible to anyone familiar with basic abstract algebra. The focus of the book is on direct sums of CS-modules and classes of modules related to CS-modules, such as relative (injective) ejective modules, (quasi) continuous modules, and lifting modules. In particular, matrix CS-rings are studied and clear proofs of fundamental decomposition results on CS-modules over commutative domains are given, thus complementing existing monographs in this area.Open problems round out the work and establish the basis for further developments in the field. The main text is complemented by a wealth of examples and exercises. |

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### Contents

1 | |

Chapter 2 Types of Relative Injectivity | 75 |

Chapter 3 Extending Property and Related Concepts | 117 |

Chapter 4 Inner Generalizations of Extending Modules | 175 |

Chapter 5 Outer Generalizations of Extending Modules | 247 |

Chapter 6 Dual Goldie and ECcomplement Versions of the Extending Property | 321 |

### Other editions - View all

Module Theory, Extending Modules and Generalizations Adnan Tercan,Canan C. Yücel No preview available - 2016 |

### Common terms and phrases

A-injective A1 and A2 A1 B A2 Abelian group Artinian Assume canonical projection complement submodule composition series condition Corollary Dedekind domain Define denote direct sum direct summand EC11-module element Elift End(RA epimorphism essential extensions essential submodule Example Exercise exists a direct exists a submodule extending modules finite uniform dimension following statements G-extending hence Homº homomorphism hypothesis idempotent implies indecomposable injective hull injective module isomorphic left ideal left Noetherian left R-module Lemma Let a e lifting Lifty matrix ring monomorphism non-zero nonsingular PI-extending positive integer Proof Proposition Prove quasi-continuous R-homomorphism result right CS-ring right ideal satisfies C11 self-injective semiprime semisimple module semisimple submodule shows socA statements are equivalent submodule A1 sum of uniform supplement Suppose Tercan Theorem torsion torsion-free uniform modules uniform submodules weak CS-module Z/Zp