| Summary: | In this paper, we provide the basic properties of (semi)simple hypermodules. We show that if a hypermodule <i>M</i> is simple, then <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>E</mi><mi>n</mi><mi>d</mi><mo>(</mo><mi>M</mi><mo>)</mo><mo>,</mo><mspace width="0.166667em"></mspace><mo>·</mo><mo>)</mo></mrow></semantics></math></inline-formula> is a group, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>E</mi><mi>n</mi><mi>d</mi><mo>(</mo><mi>M</mi><mo>)</mo></mrow></semantics></math></inline-formula> is the set of all normal endomorphisms of <i>M</i>. We prove that every simple hypermodule is normal projective with a zero singular subhypermodule. We also show that the class of semisimple hypermodules is closed under internal direct sums, factor hypermodules, and subhypermodules. In particular, we give a characterization of internal direct sums of subhypermodules of a hypermodule.
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