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In a ring the elements by which division is always possible are called the units (for example, 1 and −1 in the ring of integers). Another generalization of division to algebraic structures is the quotient group, in which the result of "division" is a group rather than a number.
In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total.Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.
The sum of two numbers is unique; there is only one correct answer for a sums. [8] When the sum of a pair of digits results in a two-digit number, the "tens" digit is referred to as the "carry digit". [9] In elementary arithmetic, students typically learn to add whole numbers and may also learn about topics such as negative numbers and fractions.
In mathematics, a basic algebraic operation is any one of the common operations of elementary algebra, which include addition, subtraction, multiplication, division, raising to a whole number power, and taking roots (fractional power). [1] These operations may be performed on numbers, in which case they are often called arithmetic operations.
Addition is an arithmetic operation in which two numbers, called the addends, are combined into a single number, called the sum. The symbol of addition is +. Examples are + = and + =. [44] The term summation is used if several additions are performed in a row. [45]
Direct sum: if E and F are two abelian groups, vector spaces, or modules, then their direct sum, denoted is an abelian group, vector space, or module (respectively) equipped with two monomorphisms: and : such that is the internal direct sum of () and ().
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Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.