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Because (Q_{j}) is the endomorphism ring of an infinite dimensional vector space, it has a right ideal which is not principal, for example its socle.
To illustrate this, Descartes explains that motion, although an attribute of Extension, is not principal, since we can only make sense of motion as occurring in an extended space.
That is why money is not principal motivator, according to Daniel Pink.
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It's not principal photography, it's the initial capture.
Certainly, attention should be devoted in the first instance to increasing taxes on homes that are not "principal private residences", in the language of the tax code.
In practical radar measurements, there will usually be targets which are not principal scatterers such as human targets inside the building.
The demands of the sickroom, even for those who are not principal caregivers, may be too distressing to meet, so even some who wish to help may flee, turn a false front, or emotionally abandon the sufferer.
"[Canadian Armed Forces] personnel were not principal combatants," Lamarre said.
Both Stark's and Engel's tax bills now specify that their Maryland homes are not principal residences.
Among those hospitalizations for which coccidioidomycosis was not principal or first additional diagnosis, it is unclear whether other principal diagnoses (such as AIDS) would have caused hospitalization in the absence of coccidioidomycosis.
These are not principals in a civilization fight.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com