Semifield vs. Field — What's the Difference?

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.

A broad, level, open expanse of land.

Synonym of hemifield

A meadow

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

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

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

A wide unbroken expanse, as of ice.

A battleground.

(Archaic) A battle.

The scene or an area of military operations or maneuvers

A background area, as on a flag, painting, or coin

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

An area or setting of practical activity or application outside an office, school, factory, or laboratory

An area or region where business activities are conducted

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

In baseball, the positions on defense or the ability to play defense

In baseball, one of the three sections of the outfield

A range, area, or subject of human activity, interest, or knowledge

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

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

The people running in an election for a political office

(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.

(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.

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

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

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

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

Made, used, or carried on in the field

Working, operating, or active in the field

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

To respond to or deal with

(Sports) To place in the playing area

To nominate in an election

To put into action; deploy

To enter (data) into a field.

To play as a fielder

A land area free of woodland, cities, and towns; an area of open country.

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

A wide, open space that is used to grow crops or to hold farm animals, usually enclosed by a fence, hedge or other barrier.

(geology) A region containing a particular mineral.

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

A place where competitive matches are carried out.

A place where a battle is fought; a battlefield.

An area reserved for playing a game or race with one’s physical force.

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

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

(metonymically) All of the competitors in any outdoor contest or trial, or all except the favourites in the betting.

Any of various figurative meanings, often dead metaphors.

(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.

Any of certain structures serving cognition.

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

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

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

To be the team catching and throwing the ball, as opposed to hitting it.

To place a team, its players, etc. in a game.

(transitive) To answer; to address.

(transitive) To defeat.

(transitive) To execute research (in the field).

To deploy in the field.

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

A piece of land of considerable size; esp., a piece inclosed for tillage or pasture.

A place where a battle is fought; also, the battle itself.

An open space; an extent; an expanse.

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).

An unresticted or favorable opportunity for action, operation, or achievement; province; room.

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

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

To take the field.

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

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

A piece of land cleared of trees and usually enclosed;

A region where a battle is being (or has been) fought;

Somewhere (away from a studio or office or library or laboratory) where practical work is done or data is collected;

A branch of knowledge;

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

A particular kind of commercial enterprise;

A particular environment or walk of life;

A piece of land prepared for playing a game;

Extensive tract of level open land;

(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;

A region in which active military operations are in progress;

All of the horses in a particular horse race

All the competitors in a particular contest or sporting event

A geographic region (land or sea) under which something valuable is found;

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

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

A place where planes take off and land

Catch or pick up (balls) in baseball or cricket

Play as a fielder

Answer adequately or successfully;

Select (a team or individual player) for a game;