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peteryellow
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Can you find an example of a simple domain not being skew field?
A simple domain is a mathematical structure known as a division ring, which is a generalization of a field. It is a set of elements with operations of addition, subtraction, multiplication, and division that follow specific properties.
A simple domain is a special type of skew field, in which every nonzero element has a multiplicative inverse. In other words, every element can be multiplied by a unique element to obtain the identity element. This property is not always true in a skew field.
Yes, a simple domain can be finite. For example, the integers modulo a prime number form a finite simple domain. However, most simple domains are infinite, such as the real or complex numbers.
The most well-known example of a simple domain is the field of real numbers. Other examples include the complex numbers, quaternions, and octonions. The integers modulo a prime number and the rational numbers are also simple domains.
A simple domain not being a skew field means that it does not have the property of commutativity, where the order of multiplication does not matter. This can have important implications in certain mathematical structures and applications, such as in abstract algebra and physics.