Ads
related to: zero divisors calculator multiplication worksheet free 4th grade national park passadventureacademy.com has been visited by 10K+ users in the past month
Search results
Results From The WOW.Com Content Network
In algebra, the zero-product property states that the product of two nonzero elements is nonzero. In other words, =, = = This property is also known as the rule of zero product, the null factor law, the multiplication property of zero, the nonexistence of nontrivial zero divisors, or one of the two zero-factor properties. [1]
An element that is a left or a right zero divisor is simply called a zero divisor. [2] An element a that is both a left and a right zero divisor is called a two-sided zero divisor (the nonzero x such that ax = 0 may be different from the nonzero y such that ya = 0). If the ring is commutative, then the left and right zero divisors are the same.
The graph of all zero divisors is non-empty for every ring that is not an integral domain. It remains connected, has diameter at most three, [3] and (if it contains a cycle) has girth at most four. [4] [5] The zero-divisor graph of a ring that is not an integral domain is finite if and only if the ring is finite. [3]
In an equation =, a is the dividend, b the divisor, and c the quotient. Division by zero is considered impossible at an elementary arithmetic level. Two numbers can be divided on paper using long division. An abbreviated version of long division, short division, can be used for smaller divisors.
Considered with the operations of component-wise addition, and multiplication according to the quaternion group, this collection forms a 4-dimensional algebra over the complex numbers C. The algebra of biquaternions is associative, but not commutative. A biquaternion is either a unit or a zero divisor.
In these enlarged number systems, division is the inverse operation to multiplication, that is a = c / b means a × b = c, as long as b is not zero. If b = 0, then this is a division by zero, which is not defined. [a] [4]: 246 In the 21-apples example, everyone would receive 5 apple and a quarter of an apple, thus avoiding any leftover.