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Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
Microsoft Math contains features that are designed to assist in solving mathematics, science, and tech-related problems, as well as to educate the user. The application features such tools as a graphing calculator and a unit converter. It also includes a triangle solver and an equation solver that provides step-by-step solutions to each problem.
Examples of separable extensions are many including first separable algebras where R is a separable algebra and S = 1 times the ground field. Any ring R with elements a and b satisfying ab = 1 , but ba different from 1, is a separable extension over the subring S generated by 1 and bRa .
In field theory, a branch of algebra, an algebraic field extension / is called a separable extension if for every , the minimal polynomial of over F is a separable polynomial (i.e., its formal derivative is not the zero polynomial, or equivalently it has no repeated roots in any extension field). [1]
An algebraic extension is a purely inseparable extension if and only if for every , the minimal polynomial of over F is not a separable polynomial. [1] If F is any field, the trivial extension is purely inseparable; for the field F to possess a non-trivial purely inseparable extension, it must be imperfect as outlined in the above section.
In field theory, the primitive element theorem states that every finite separable field extension is simple, i.e. generated by a single element.This theorem implies in particular that all algebraic number fields over the rational numbers, and all extensions in which both fields are finite, are simple.