The difference between Commutative ring and Field

Commutative ring as a noun (algebra, ring theory):

A ring whose multiplicative operation is commutative.

Field as a noun (usually, plural):

A land area free of woodland, cities, and towns; open country. The open country near or belonging to a town or city. # An airfield, airport or air base; especially, one with unpaved runways.

Field as a noun (geology):

A wide, open space that is usually used to grow crops or to hold farm animals. A region containing a particular mineral.

Field as a noun (baseball, obsolete):

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. # The team in a match that throws the ball and tries to catch it when it is hit by the other team (the bat). # The outfield. A place where competitive matches are carried out with figures, playing field, in a boardgame or in a computer game. A competitive situation, circumstances in which one faces conflicting moves of rivals. All of the competitors in any outdoor contest or trial, or all except the favourites in the betting.

Field as a noun (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. # The extent of a given perception. # A realm of practical, direct or natural operation, contrasted with an office, classroom, or laboratory. # A domain of study, knowledge or practice. #* {{quote-journal|lang=en|date=2013-05-10|author=Audrey Garric |volume=188|issue=22|page=30|magazine= |title=[http://www.guardian.co.uk/environment/2013/may/04/paris-green-roofs-building-climate-environment Urban canopies let nature bloom] |passage=As towns continue to grow, replanting vegetation has become a form of urban utopia and green roofs are spreading fast. Last year 1m square metres of plant-covered roofing was built in France, as much as in the US, and 10 times more than in Germany, the pioneer in this field.}} # An unrestricted or favourable opportunity for action, operation, or achievement. #* |title=The History Of England From the Accession of James II|volume=1|chapter=IV|year=1848|passage=Penn was without doubt a man of eminent virtues. He had a strong sense of religious duty and a fervent desire to promote the happiness of mankind. On one or two points of high importance, he had notions more correct than were, in his day, common even among men of enlarged minds: and as the proprietor and legislator of a province which, being almost uninhabited when it came into his possession, afforded a clear field for moral experiments, he had the rare good fortune of being able to carry his theories into practice without any compromise, and yet without any shock to existing institutions.}} #* |title=The Way We Live Now|year=1875|section=Chap. II|passage=Tidings had reached her of this and the other man's success, and,—coming near to her still,—of this and that other woman's earnings in literature. And it had seemed to her that, within moderate limits, she might give a wide field to her hopes.}} # A commutative ring satisfying the field axioms. A physical or virtual location for the input of information in the form of symbols. # The background of the shield. # The background of the flag. # A concrete section in a form which is supposed to be filled with data. #* [https://www.w3schools.com/php/php_form_required.asp PHP 5 Forms Required Fields] at W3Schools #*: From the validation rules table on the previous page, we see that the "Name", "E-mail", and "Gender" fields are required. These fields cannot be empty and must be filled out in the HTML form. # A component of a database in which a single unit of information is stored. ## An area of memory or storage reserved for a particular value, subject to virtual access controls.

Field as a verb (transitive, sports):

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

Field as a verb (baseball, softball, cricket, and other batting sports):

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

Field as a verb (transitive, sports):

To place a team in (a game).

Field as a verb (transitive):

To answer; to address.

Field as a verb (transitive):

To defeat.

Field as a verb (transitive):

To execute research (in the field).

Field as a verb (transitive, military):

To deploy in the field.