# Semifield vs. Field — What's the Difference?

## Definitions

#### Semifield➦

In mathematics, a semifield is an algebraic structure with two binary operations, addition and multiplication, which is similar to a field, but with some axioms relaxed.

#### Field➦

A broad, level, open expanse of land.

#### Semifield➦

Synonym of hemifield

#### Field➦

Cows grazing in a field.

#### Semifield➦

(mathematics) An algebraic structure with two binary operations, addition and multiplication, similar to the field but with some axioms relaxed.

#### Field➦

A cultivated expanse of land, especially one devoted to a particular crop
A field of corn.

#### Field➦

A portion of land or a geologic formation containing a specified natural resource
A copper field.

#### Field➦

A wide unbroken expanse, as of ice.

A battleground.

#### Field➦

(Archaic) A battle.

#### Field➦

The scene or an area of military operations or maneuvers
Officers in the field.

#### Field➦

A background area, as on a flag, painting, or coin
A blue insignia on a field of red.

#### Field➦

(Heraldry) The background of a shield or one of the divisions of the background.

#### Field➦

An area or setting of practical activity or application outside an office, school, factory, or laboratory
Biologists working in the field.
A product tested in the field.

#### Field➦

An area or region where business activities are conducted
Sales representatives in the field.

#### Field➦

An area in which an athletic event takes place, especially the area inside or near to a running track, where field events are held.

#### Field➦

In baseball, the positions on defense or the ability to play defense
She excels in the field.

#### Field➦

In baseball, one of the three sections of the outfield
He can hit to any field.

#### Field➦

A range, area, or subject of human activity, interest, or knowledge
Several fields of endeavor.

#### Field➦

The contestants or participants in a competition or athletic event, especially those other than the favorite or winner.

#### Field➦

The body of riders following a pack of hounds in hunting.

#### Field➦

The people running in an election for a political office
The field has been reduced to three candidates.

#### Field➦

(Mathematics) A set of elements having two operations, designated addition and multiplication, satisfying the conditions that multiplication is distributive over addition, that the set is a group under addition, and that the elements with the exception of the additive identity form a group under multiplication.

#### Field➦

(Physics) A physical quantity in a region of space, such as gravitational force or fluid pressure, having a distinct value (scalar, vector, or tensor) at each point.

#### Field➦

The usually circular area in which the image is rendered by the lens system of an optical instrument; field of view.

#### Field➦

An element of a database record in which one piece of information is stored.

#### Field➦

A space, as on an online form or request for information, that accepts the input of text

#### Field➦

Growing, cultivated, or living in fields or open land.

#### Field➦

Made, used, or carried on in the field
Field operations.

#### Field➦

Working, operating, or active in the field
Field representatives of a firm.

#### Field➦

(Sports) To catch or pick up (a ball) and often make a throw to another player, especially in baseball.

#### Field➦

To respond to or deal with
Fielded tough questions from the press.

#### Field➦

(Sports) To place in the playing area
Field a team.

#### Field➦

To nominate in an election
Field a candidate.

#### Field➦

To put into action; deploy
Field an army of campaign workers.

#### Field➦

To enter (data) into a field.

#### Field➦

To play as a fielder
How well can he field?.

#### Field➦

A land area free of woodland, cities, and towns; an area of open country.
There are several species of wild flowers growing in this field.

#### Field➦

The open country near or belonging to a town or city.

#### Field➦

A wide, open space that is used to grow crops or to hold farm animals, usually enclosed by a fence, hedge or other barrier.
There were some cows grazing in a field.
A crop circle was made in a corn field.

#### Field➦

(geology) A region containing a particular mineral.
An oil field; a gold field

#### Field➦

An airfield, airport or air base; especially, one with unpaved runways.

#### Field➦

A place where competitive matches are carried out.

#### Field➦

A place where a battle is fought; a battlefield.

#### Field➦

An area reserved for playing a game or race with one’s physical force.
Soccer field
Substitutes are only allowed onto the field after their boots are checked.

#### Field➦

A place where competitive matches are carried out with figures, or playing area in a board game or a computer game.

#### Field➦

A competitive situation, circumstances in which one faces conflicting moves of rivals.

#### Field➦

(metonymically) All of the competitors in any outdoor contest or trial, or all except the favourites in the betting.
This racehorse is the strongest in a weak field.

#### Field➦

Any of various figurative meanings, often dead metaphors.

#### Field➦

(physics) A physical phenomenon (such as force, potential or fluid velocity) that pervades a region; a mathematical model of such a phenomenon that associates each point and time with a scalar, vector or tensor quantity.
Magnetic field; gravitational field; scalar field

#### Field➦

Any of certain structures serving cognition.

#### Field➦

A physical or virtual location for the input of information in the form of symbols.

#### Field➦

Part (usually one half) of a frame in an interlaced signal

#### Field➦

To intercept or catch (a ball) and play it.

#### Field➦

To be the team catching and throwing the ball, as opposed to hitting it.
The blue team are fielding first, while the reds are batting.

#### Field➦

To place a team, its players, etc. in a game.
The away team fielded two new players and the second-choice goalkeeper.

#### Field➦

She will field questions immediately after her presentation.

#### Field➦

(transitive) To defeat.
They fielded a fearsome army.

#### Field➦

(transitive) To execute research (in the field).
He fielded the marketing survey about the upcoming product.

#### Field➦

To deploy in the field.
To field a new land-mine detector

#### Field➦

Cleared land; land suitable for tillage or pasture; cultivated ground; the open country.

#### Field➦

A piece of land of considerable size; esp., a piece inclosed for tillage or pasture.
Fields which promise corn and wine.

#### Field➦

A place where a battle is fought; also, the battle itself.
In this glorious and well-foughten field.
What though the field be lost?

#### Field➦

An open space; an extent; an expanse.
Without covering, save yon field of stars.
Ask of yonder argent fields above.

#### Field➦

The whole surface of an escutcheon; also, so much of it is shown unconcealed by the different bearings upon it. See Illust. of Fess, where the field is represented as gules (red), while the fess is argent (silver).

#### Field➦

An unresticted or favorable opportunity for action, operation, or achievement; province; room.
Afforded a clear field for moral experiments.

#### Field➦

A collective term for all the competitors in any outdoor contest or trial, or for all except the favorites in the betting.

#### Field➦

That part of the grounds reserved for the players which is outside of the diamond; - called also outfield.

#### Field➦

To take the field.

#### Field➦

To stand out in the field, ready to catch, stop, or throw the ball.

#### Field➦

To catch, stop, throw, etc. (the ball), as a fielder.

#### Field➦

A piece of land cleared of trees and usually enclosed;
He planted a field of wheat

#### Field➦

A region where a battle is being (or has been) fought;
They made a tour of Civil War battlefields

#### Field➦

Somewhere (away from a studio or office or library or laboratory) where practical work is done or data is collected;
Anthropologists do much of their work in the field

#### Field➦

A branch of knowledge;
In what discipline is his doctorate?
Teachers should be well trained in their subject
Anthropology is the study of human beings

#### Field➦

The space around a radiating body within which its electromagnetic oscillations can exert force on another similar body not in contact with it

#### Field➦

A particular kind of commercial enterprise;
They are outstanding in their field

#### Field➦

A particular environment or walk of life;
His social sphere is limited
It was a closed area of employment
He's out of my orbit

#### Field➦

A piece of land prepared for playing a game;
The home crowd cheered when Princeton took the field

#### Field➦

Extensive tract of level open land;
They emerged from the woods onto a vast open plain
He longed for the fields of his youth

#### Field➦

(mathematics) a set of elements such that addition and multiplication are commutative and associative and multiplication is distributive over addition and there are two elements 0 and 1;
The set of all rational numbers is a field

#### Field➦

A region in which active military operations are in progress;
The army was in the field awaiting action
He served in the Vietnam theater for three years

#### Field➦

All of the horses in a particular horse race

#### Field➦

All the competitors in a particular contest or sporting event

#### Field➦

A geographic region (land or sea) under which something valuable is found;
The diamond fields of South Africa

#### Field➦

(computer science) a set of one or more adjacent characters comprising a unit of information

#### Field➦

The area that is visible (as through an optical instrument)

#### Field➦

A place where planes take off and land

#### Field➦

Catch or pick up (balls) in baseball or cricket

#### Field➦

Play as a fielder