separable extension

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separable extension

[′sep·rə·bəl ik′sten·chən]
(mathematics)
A field extension K of a field F is separable if every element of K is a root of a separable polynomial whose coefficients are elements of F.
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Being an inseparable extension of the nervous system, an injury to the spine can render a person, temporarily or permanently, at partial or complete loss of muscle function, sensation, autonomic function of a part of the body, affecting adversely the life of the victim.
Vikrant Gandhi, Strategic Industry Analyst in Mobile Communications for Frost & Sullivan, an analyst firm based in Palo Alto, California, commented, "Cell phones are fast becoming an inseparable extension of teens and young adults today; using text to reach each other on their phones is an important form of social communication.
Among the topics are genus change in inseparable extensions of functional fields, the homology of noetherian rings and local rings, the cohomology groups of tori in infinite Galois extensions of number fields, an algorithm for determining the type of a singular fiber in an elliptic pencil, variation of the canonical height of a point depending on a parameter, the non-existence of certain Galois extensions of Q unramified outside two, and refining Gross' conjecture on the values of abelian L-functions.