ADS modules
Copyright policy )ADS modules
We study the class of ADS rings and modules introduced by Fuchs. We give some connections between this notion and classical notions such as injectivity and quasi-continuity. A simple ring R such that R is ADS as a right R-module must be either right self-injective or indecomposable as a right R-module. Under certain conditions we can construct a unique ADS hull up to isomorphism. We introduce the concept of completely ADS modules and characterize completely ADS semiperfect right modules as direct sum of semisimple and local modules.
7 pages
- Artois University France
- King Abdulaziz University Saudi Arabia
- Ohio University United States
- University System of Ohio United States
Injective modules, Algebra and Number Theory, quasi-continuous modules, [MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA], ADS modules, injective modules, relative injective, Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras), Mathematics - Rings and Algebras, absolute direct summand property, Other classes of modules and ideals in associative algebras, Modules, 510, Direct sums, Injective, CS modules, Quasi-continuous modules, Rings and Algebras (math.RA), Injective modules, self-injective associative rings, [MATH.MATH-RA] Mathematics [math]/Rings and Algebras [math.RA], FOS: Mathematics, direct sums, ADS hulls
Injective modules, Algebra and Number Theory, quasi-continuous modules, [MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA], ADS modules, injective modules, relative injective, Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras), Mathematics - Rings and Algebras, absolute direct summand property, Other classes of modules and ideals in associative algebras, Modules, 510, Direct sums, Injective, CS modules, Quasi-continuous modules, Rings and Algebras (math.RA), Injective modules, self-injective associative rings, [MATH.MATH-RA] Mathematics [math]/Rings and Algebras [math.RA], FOS: Mathematics, direct sums, ADS hulls
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