On H-µ-supplemented modules

الملخص EN

Weosay thatotheosubmodules A, B ofoan R-module Moare µ-equivalent , AµB ifoand onlyoif <<µand <<µ.

Weoshow thatoµ relationois anoequivalent relationoand hasegood behaviorywith respectyto additionmof submodules, homorphismsr, andydirectusums, weaapplyothese resultsotoointroduced theoclassoof H-µ-supplementedomodules.

Weosay thatoa module Mmis H-µ-supplementedomodule ifofor everyosubmodule A of M, thereois a directosummand D ofoM suchothat AµD.

Variousoproperties ofothese modulesoarepgiven.