general

definition of algebra

Algebra is known as the area of ​​mathematics responsible for the investigation of structures, relationships and quantities. In algebra and unlike arithmetic that does use numbers, these are replaced by symbols, for several reasons, first because it will be easier to formulate general laws of arithmetic, for example a + b = b + a, second because it will allow referring to unknown numbers, formulating equations and studying how to solve them and finally because the symbols are more Functional when formulating functional relationships, forgive the redundancy.

On the other hand, algebraic structures are a set of elements that have certain operational properties, while what will define the structure are those operations that can be performed with the elements that make up said set and the mathematical properties that these operations entail. Among the most common algebraic structures we can mention: the group, ring, body, monoid, vector space, module, among others.

As we said above, algebra makes use of various signs and symbols which of course, within the algebraic context, will have a certain meaning. For example, the sign + expresses addition and is used to express binary operations, the first letters of the alphabet to express known quantities, while the last letters serve, on the contrary, to refer to the unknowns, the letter n is known It will be used when you want to express any quantity and co to k to refer to constant terms, among others.

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