St-closed Submodules and Semi-extending Modules

Riadh Abbas, Maysaa; Abbas Ahmed, Muna

ISBN 10: 3659864072 / ISBN 13: 9783659864070

Editore: LAP LAMBERT Academic Publishing, 2016

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Codice articolo 26396998622

Dati bibliografici

• Titolo: St-closed Submodules and Semi-extending Modules
• Editore: LAP LAMBERT Academic Publishing
• Data di pubblicazione: 2016
• Lingua: Inglese
• ISBN 10: 3659864072
• ISBN 13: 9783659864070
• Rilegatura: Brossura
• Condizione: New

Descrizione articolo

Riassunto

The main purpose of this work is to determine and study two new concepts (up to our knowledge) which are St-closed submodules and semi-extending modules. St-closed submodules is contained properly in the class of closed submodules, where a submodule N of M is called St-closed in M, if N has no proper semi-essential extension in M, i.e if there exists a submodule K of M such that N is a semi-essential submodule of K, then N = K. We investigate the main properties of this type of submodules, and discuss some results that are useful in our work. The class of semi-extending modules is a generalization to the notion of extending modules, where an R-module M is called semi-extending, if every submodule of M is a semi-essential in a direct summand of M. Various properties of semi-extending modules are obtained, and we study the relationships between this class of modules and other related concepts.