Bookcover of Some Generalizations of Quasi-Dedekind Modules
Booktitle:

Some Generalizations of Quasi-Dedekind Modules

LAP LAMBERT Academic Publishing (2016-07-21 )

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ISBN-13:

978-3-659-91826-1

ISBN-10:
3659918261
EAN:
9783659918261
Book language:
English
Blurb/Shorttext:
A module M over a associative ring with unity R is called quasi-Dedekind if every nonzero submodule of M is quasi-invertible (Equivalently a module M is quasi-Dedekind if for any nonzero homomorphism f from M to itself, f is monomorphism). In this book we study essentially quasi-Dedekind modules as a generalization of quasi-Dedekind modules, where an R-module M is said to be essentially quasi-Dedekind if every essential submodule of M is quasi-invertible. We prove that this concept is equivalent to the concept K-nonsingular modules, where a module M is said to be K-nonsingular if for each nonzero homomorphism f from M to itself implies Kerf is not essential in M. We studied the relationships between this concept and several other types of modules such as: quasi-Dedekind, prime, essentially prime, scalar, nonsingular, monoform, Baer and compressible modules,… etc. Beside, we present the concept of small quasi-Dedekind module as another generalization of quasi-Dedekind module, where an R-module M is called small quasi-Dedekind if for each nonzero homomorphism f from M to itself, Kerf is small in M.
Publishing house:
LAP LAMBERT Academic Publishing
Website:
https://www.lap-publishing.com/
By (author) :
Tha'ar Younis Ghawi, Inaam M-A Hadi
Number of pages:
136
Published on:
2016-07-21
Stock:
Available
Category:
Arithmetic, Algebra
Price:
55.90 €
Keywords:
Essentially quasi-invertible submodules, Essentially quasi-Dedikind modules, Essentially prime Modules, Small quasi-Dedekind modules, Small monoform modules

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