%0 Journal Article
%T The <i>Njiki</i>&#8217;s Fundamental Theorem-Definition on Fractions in the <i>Mathematical</i> Set <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'> <mi>&#x211A;</mi></math> and by <i>Extension</i> in <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'> <mi>&#x211D;</mi></math> and <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'> <mi>&#x2102;</mi></math>, for the Purpose of Leading to the Construction of Some Algebraic Structures as Its Theoretical Applications and for the Practical Ones
%A Jean Claude Njiki
%J American Journal of Computational Mathematics
%P 358-379
%@ 2161-1211
%D 2024
%I Scientific Research Publishing
%R 10.4236/ajcm.2024.143018
%X The purpose of the research in the <i>NJIKI</i>&#8217;s fundamental THEOREM-DEFINITION on fractions in the mathematical set <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mi>&#x211A;</mi>
</math>

 and by extension in <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mi>&#x211D;</mi>
</math>

 and <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mi>&#x2102;</mi>
</math>

 and in order to construct some algebraic structures is about the proved EXISTENCE and the DEFINITION by <i>NJIKI</i> of two INNOVATIVE, IMPORTANT and TEACHABLE operations of addition or additive operations, in <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mi>&#x211A;</mi>
</math>

, marked <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mo>&#x2295;</mo>
</math>

 and <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <msub>
   <mo>+</mo>
   <mrow>
    <mi>&#x03B1;</mi><mo>,</mo><mi>&#x03B2;</mi></mrow>
  </msub>
  </mrow>
</math>

, and taken as VECTORIAL, TRIANGULAR, of THREE or PROPORTIONAL operations and in order to make THEM not be different from the RATIONAL ONE, +, but to bring much more and new information on fractions, and, by extension in <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mi>&#x211D;</mi>
</math>

 and <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mi>&#x2102;</mi>
</math>

. And the very <i>NJIKI</i>&#8217;s fundamental THEOREM-DEFINITION having many APPLICATIONS in the everyday life of the HUMAN BEINGS and without talking about computer sciences, henceforth being supplied with very interesting new ALGORITHMS. And as for the work done in the research, it will be waiting for its extension to be done after publication and along with the research results concerned.
%K Operations of Addition
%K <i>Additive</i> Operations in <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'> <mi>&#x211A
%K </mi></math>
%K Laws in <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'> <mi>&#x211A
%K </mi></math>
%K THEOREM-DEFINITION
%K External Multiplication
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=136431