"From where they're situated, they have a perfect field of fire."

The same is true if the complex numbers are replaced by a perfect field with a valuation.

They would give him a perfect field of fire on the front door and half of the windows facing the street.

Never a ripple, just shirts like perfect fields of snow.

A primary extension of a perfect field is regular.

Smooth completions exist and are unique over a perfect field.

The rocky, tumbled ground was a perfect field of war for the Highlanders.

Start with the category Sm of smooth varieties over a perfect field.

The flaming wagons gave a perfect field of fire and the Germans suffered heavy losses.

To Dar, it looked as if someone had kicked a crucifix for a perfect field goal.

Consider linear operators on a finite-dimensional vector space over a perfect field.

Let be a reduced and connected scheme over a perfect field endowed with a section .

They'd have been perfect field viewing astronomical glasses, except that there were always clouds and Tim rarely saw the stars.

Over a perfect field, all irreducible polynomials are separable, so that condition is also necessary.

Friends and family members say Ms. Rosenthal, who defends the legal rights of foster care children, has found the perfect field for her personality.

The path stretched down the hill and across perfect fields, just irregular enough to be charming, divided one from another by old-fashioned English hedgerows.

Any finitely generated field extension over a perfect field is separably generated.

Examples of perfect fields are:

Any differentially perfect field K has a differential closure, a prime model extension, which is differentially closed.

All of the SEALS, scattered as they were, had perfect fields of fire.

The Sisko looks around the perfect field, inhales the rich scent of the grass, hears the growing tumult of the crowd.

An algebraic closure of an arbitrary field is Galois over if and only if is a perfect field.

A few weeks later he crammed most of the neighborhood into his 1934 Plymouth and set in search of the perfect field and the perfect game.

The separable closure is the full algebraic closure if and only if K is a perfect field.

More precisely, a point in a variety (over a perfect field) is smooth if the local ring at the point is a regular local ring.