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The difference quotient is sometimes also called the Newton quotient [10] [12] [13] [14] (after Isaac Newton) or Fermat's difference quotient (after Pierre de Fermat ).
Semisimple rings are of particular interest to algebraists. For example, if the base ring R is semisimple, then all R -modules would automatically be semisimple. Furthermore, every simple (left) R -module is isomorphic to a minimal left ideal of R, that is, R is a left Kasch ring .
Long division. In arithmetic, long division is a standard division algorithm suitable for dividing multi-digit Hindu-Arabic numerals ( Positional notation) that is simple enough to perform by hand. It breaks down a division problem into a series of easier steps.
The regular open sets of any topological space form a complete Boolean algebra. This example is of particular importance because every forcing poset can be considered as a topological space (a base for the topology consisting of sets that are the set of all elements less than or equal to a given element). The corresponding regular open algebra can be used to form Boolean-valued models which ...
Quotient ring. In ring theory, a branch of abstract algebra, a quotient ring, also known as factor ring, difference ring [1] or residue class ring, is a construction quite similar to the quotient group in group theory and to the quotient space in linear algebra. [2] [3] It is a specific example of a quotient, as viewed from the general setting ...
A division algorithm is an algorithm which, given two integers N and D (respectively the numerator and the denominator), computes their quotient and/or remainder, the result of Euclidean division. Some are applied by hand, while others are employed by digital circuit designs and software. Division algorithms fall into two main categories: slow ...
Classification of finite simple groups. In mathematics, the classification of finite simple groups is a result of group theory stating that every finite simple group is either cyclic, or alternating, or belongs to a broad infinite class called the groups of Lie type, or else it is one of twenty-six or twenty-seven exceptions, called sporadic.
Quotient space (linear algebra) In linear algebra, the quotient of a vector space by a subspace is a vector space obtained by "collapsing" to zero. The space obtained is called a quotient space and is denoted (read " mod " or " by ").