| Summary: | The primary motivation of this article is to introduce the definition of a strongly belonging element of a brace, presenting some results concerning the case where <i>I</i> acts as an ideal of a brace, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>A</mi><mo>,</mo><mo>+</mo><mo>,</mo><mo>∘</mo><mo>)</mo></mrow></semantics></math></inline-formula>. We find that an element <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mo>∈</mo><mi>I</mi></mrow></semantics></math></inline-formula> acts as strongly belonging element of <i>I</i> when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mo>+</mo><mi>b</mi></mrow></semantics></math></inline-formula> yields <i>a</i> for all <i>b</i> in <i>I</i>.
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