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The English word "algebra" is a translation of the Arabic title of a treatise by al-Khwrizm on algebraic techniques. The word "algebra" has numerous meanings today.
The abstract study of number systems and processes, including more complex topics such as groups, rings, invariant theory, and cohomology, is an application of the word "algebra." This is the definition of "algebra" used by mathematicians. This area of mathematics is often called abstract algebra when there is a possibility of misunderstanding.
The term "algebra" can also refer to "school algebra" typically taught in middle and high schools in the United States. This covers the fundamental features of functions and graphs, as well as the solution of polynomial equations in one or more variables. Mathematicians refer to this subject as "school algebra," "elementary algebra," "high school algebra," "high school algebra," or simply "algebra." They reserve the term "algebra" for the more complex facets of the subject. At home you can train in algebra with the Alicia division calculator .
The word is also used in a third context, this time as an algebraic structure rather than a subject. Formally speaking, the algebra is a multiplication on a vector space V over a field F. Each f in F and x, y in V must hold for the multiplication to be distributive.
f(xy)=(fx)y=x(fy).
Sometimes the associative or multiplicative identities of an algebra are implicitly assumed.
The algebra of real numbers, vectors and matrices, tensors, complex numbers, and quaternions are some examples of algebra. (Note that linear algebra is not algebra in the formal sense of the word; it is the study of linear sets of equations and their transformation characteristics.) The names of one or more of its researchers are usually attached to other, more unusual algebras. that have been studied and found to be of interest. Unfortunately, this method results in completely meaningless names that algebraists frequently employ without further justification or clarification.
Editorial: silvio
Año de publicación: 2022
Características de la edición del libro:
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Género: Matemáticas
Tema informativo: Educación
Tags: Matemáticas
