ABSOLUTE FIELD Meaning and
Definition
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An absolute field is a concept in mathematics that refers to a particular type of field where every non-zero element has a unique multiplicative inverse. In other words, for every non-zero element a in an absolute field, there exists a unique element b such that the product of a and b is equal to the multiplicative identity element of the field, usually denoted by 1.
One characteristic feature of an absolute field is that the elements within it can be added, subtracted, multiplied, and divided, with the exception of division by zero which is undefined. Moreover, an absolute field also satisfies all the properties of a general field, including the commutative, associative, and distributive laws.
Examples of absolute fields include the rational numbers, the real numbers, and the complex numbers. These fields have the property that every non-zero element can be inverted and that the inverse is unique. Conversely, fields that do not satisfy this property are called non-absolute fields.
Understanding the concept of an absolute field is crucial in many areas of mathematical study, particularly in algebra and number theory. It provides a fundamental framework for exploring the properties and behaviors of various mathematical objects, making it an indispensable concept in mathematical analysis and problem-solving.
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That portion of the cerebral cortex, a lesion of which invariably produces spasm or paralysis.
A practical medical dictionary. By Stedman, Thomas Lathrop. Published 1920.
Common Misspellings for ABSOLUTE FIELD
- zbsolute field
- sbsolute field
- wbsolute field
- qbsolute field
- avsolute field
- ansolute field
- ahsolute field
- agsolute field
- abaolute field
- abzolute field
- abxolute field
- abdolute field
- abeolute field
- abwolute field
- absilute field
- absklute field
- absllute field
- absplute field
- abs0lute field
- abs9lute field
Etymology of ABSOLUTE FIELD
The term "absolute field" does not have an etymology on its own, as it is a combination of two separate words: "absolute" and "field", each with their own etymologies.
- "Absolute" comes from the Latin word "absolutus", which means "loosened" or "released", derived from the verb "absolvere", meaning "to set free" or "to complete". Over time, "absolute" in English has come to mean "unrestricted", "unchanging", or "not dependent on anything else".
- "Field" originates from the Old English word "feld", which referred to an empty, open space of land. This word is connected to the Old High German term "feld", the Old Norse word "vǫllr", and the Gothic word "falds", all of which share a similar root meaning "field" or "meadow".
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