On Strongly Extending Modules
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The purpose of this paper is to introduce the concept ofstrongly extending modules which are particular subclass of theclass of extending modules, and study some basic properties ofthis new class of modules. A module M is called stronglyextending if each submodule of M is essential in a fullyinvariant direct summand of M. In this paper we examine thebehavior of the class of strongly extending modules with respectto the preservation of this property in direct summands anddirect sums and give some properties of these modules, forinstance, strongly summand intersection property and weaklyco-Hopfian property. Also such modules are characterized overcommutative Dedekind domains.
Abstract
The purpose of this paper is to introduce the concept ofstrongly extending modules which are particular subclass of theclass of extending modules, and study some basic properties ofthis new class of modules. A module M is called stronglyextending if each submodule of M is essential in a fullyinvariant direct summand of M. In this paper we examine thebehavior of the class of strongly extending modules with respectto the preservation of this property in direct summands anddirect sums and give some properties of these modules, forinstance, strongly summand intersection property and weaklyco-Hopfian property. Also such modules are characterized overcommutative Dedekind domains.
참고문헌 (15)
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