Principal ideal domains are thus mathematical objects which behave somewhat like the integers, with respect to divisibility: any element of a PID has a unique decomposition into prime elements ( so an analogue of the fundamental theorem of arithmetic holds ); any two elements of a PID have a greatest common divisor ( although it may not be possible to find it using the Euclidean algorithm ).

Principal ideal domains are noetherian, they are integrally closed, they are unique factorization domains and Dedekind rings.

** Principal ideal domain, an integral domain in which every ideal is principal

Principal ideal domains are integral domains in which every ideal can be generated by a single element, another property shared by the integers.

* Principal ideal, an ideal with a single generator, and the related concept of principal ideal domains

The Principal, a staff advisor, Dean of students, Dean of Women students, NSS Program officer, Toppers, Cultural Centre student representative, Gymkhana student representative, NSS student representative, 2 women student representatives form an integral part of the Council.

In the following year he became provisional Principal of the Theological College of Saint Thomas ( from which he had just graduated ), and in 1903 his appointment was made permanent.

The use of only the top three strings was popular for bass soloists and Principal bassists in orchestras in the 19th century, because it reduced the pressure on the wooden top of the bass, which was thought to create a more resonant sound.

He acquired his Ph. D. in 1900 after which he took his first school job a Principal in a St. Louis, Missouri Elementary School.

The only surviving complete works by Epicurus are three letters, which are to be found in book X of Diogenes Laertius ' Lives of Eminent Philosophers, and two groups of quotes: the Principal Doctrines, reported as well in Diogenes ' book X, and the Vatican Sayings, preserved in a manuscript from the Vatican Library.

Following the introduction of the Criminal Justice Act 2006 and its extensive and complex rewriting of the Firearms Act, the Minister for Justice at the time ( Micheal McDowell ) instituted the Firearms Consultation Panel, a panel chaired by the Minster through the Principal Officer of the Department of Justice's Firearms Section, which comprised representatives from the Gardai, Department of Sport, firearms dealers, all the national governing bodies of the shooting sports, and other stakeholders in the Firearms Act ( such as insurance providers ).

Principal liturgical forms which endured throughout the entire Renaissance period were masses and motets, with some other developments towards the end, especially as composers of sacred music began to adopt secular forms ( such as the madrigal ) for their own designs.

Each head of family received a ballot which contained two questions: the first asking if the Government of San Marino should be headed by a Principal and Sovereign Council, and the second, if the number of members of the Council should be proportionate between the city population and the rural population.

that nations based on respect for the principle of equal rights and fair equality of opportunity have the right to freely choose their sovereignty and international political status with no external compulsion or interference which can be traced back to the Atlantic Charter, signed on 14 August 1941, by Franklin D. Roosevelt, President of the United States of America, and Winston Churchill, Prime Minister of the United Kingdom pledged The Eight Principal points of the Charter.

By 1966 all non-degree courses were moved to the Manchester Polytechnic which is now known as Manchester Metropolitan University, and in 1966 the name finally changed to the University of Manchester Institute of Science and Technology on the initiative of Acting Principal Frank Morton.

* In The Simpsons episode, " Holidays of Future Passed ", the episode set in December 2041, Bart is a deadbeat dad living in Springfield Elementary ( which is now an apartment complex instead of a school ) with Principal Skinner as his landlord.

The Cherokee refer to themselves as Tsalagi () or Aniyvwiyaʔi (), which means " Principal People.

In the Principal Register, a registrant gains nationwide constructive use and constructive notice, which prevent others from using or registering that registrant ’ s trade dress ( without contesting the registration ).

Further, a registrant in the Principal Register gains incontestable status after five years, which eliminates many of the ways for another party to challenge the registration.

* In The Simpsons episode, " Holidays of Future Passed ", the episode set in December 2041, Bart is a deadbeat dad living in Springfield Elementary ( which is now an apartment complex instead of a school ) with Principal Skinner as his landlord.

According to the episode " Principal Charming ", his name was Ralph Melish, which is a reference to the Monty Python sketch " The Adventures of Ralph Melish: Hot Dog and Knickers " from The Monty Python Matching Tie and Handkerchief.

Principal photography began on 19 May 1976 on the South Fork of Long Island with the scene in which Alvy and Annie boil live lobsters ; filming continued periodically for the next ten months.

The fire of 1984 affected the organ but not irreparably ; the damage hastened the time for a major restoration, which was begun in 1991 and finished two years later by Principal Pipe Organs of York, under the direction of their founder, Geoffrey Coffin, who had at one time been assistant organist at the Minster.

The University's first Principal, Professor Tom Cottrell, believed that art should be part of the everyday cultural experience at the University, and his inspiration led to the establishment of the MacRobert Arts Centre, which is a small theatre and cinema complex, located adjacent to the Andrew Miller Building.

The first-known English climber in the Alps was Colonel Mark Beaufoy ( 1764 – 1827 ), who in 1787 made an ascent ( the fourth ) of Mont Blanc, a mountain to which his fellow-countrymen long exclusively devoted themselves, with a few noteworthy exceptions, such as Principal J. D.

Principal photography was completed three days before the scheduled DGA strike, which ultimately failed to materialize.

They were working for the U. S. government, marking a north-south line called the Fourth Principal Meridian, from which much of the land in the state would be measured.

The San Bartolo murals have a Principal Bird Deity seated on top of each of four world trees, recalling the four world trees ( together with a fifth, central tree ) which, according to some of the early-colonial Chilam Balam books, were re-erected after the collapse of the sky.

Principal photography was scheduled to run three months but ran nine months or more due to numerous delays and setbacks ( most of which were due to Stevens ' insistence on shooting dozens of retakes in every scene ).

The new system would allow the Leader and Deputy ( or Co-Leaders ) to vote on GPEx and, rather than being elected annually ( like the Principal Speakers ), the posts would be elected every two years.

The sequestrators ensure that a minimum number of church services continues to be held in the parish, and in particular that the Eucharist continues to be celebrated every Sunday and on every Principal Feast.

The Local Managing Committee ( LMC ) comprises nine members, including the Principal as the secretary, and Rector as the chairperson, and meets twice every year.

Principal Genco and her administration implemented the Walton Plan to target lateness and loitering around campus, and to encourage the faculty to show interest in every student's progress.

Additional oversight of OTCQX securities is provided by requiring every issuer to be sponsored by approved third-party investment banks or law firms, called Principal American Liaison ( PAL ) for non-US issuers and Designated Advisors For Disclosure ( DADs ) for US issuers.

In October 2007, Principal Robert Frizelle offered to change his hair color every day for a week if the fund-raiser gathered in more than $ 18, 000 ( fund-raising had been down, with only $ 13, 000 gathered the year before ).

Principal Skinner orders a search of every student's locker, and it is discovered that Nelson Muntz is the culprit.

Under his stewardship and with Kevin Scanlon as the Principal for more than a decade, the School excelled in every way.

Van Driessen is fired from his job in the " School Test " episode by Principal McVicker, who blamed him for Beavis and Butt-Head being " so damn stupid.

Angry, impatient and short-tempered, Buzzcut is a Vietnam War veteran who served in the Marine Corps and, with the possible exception of Principal McVicker, hates the duo more than any other character.

The Principal title is often used in dual career ladder organizations and may be equivalent to manager or director.

* Principal switching center is Asunción

According to the Principal Principle, the fair price is 32 cents.

The LLNL Director is supported by a senior executive team consisting of the Deputy Director, the Deputy Director for Science and Technology, Principal Associate Directors, and other senior executives who manage areas / functions directly reporting to the Laboratory Director.

The Laboratory is organized into four principal directorates, each headed by a Principal Associate Director:

He himself is referring to those in his Epitome to Herodotus and in Principal Doctrines.

The President of the Senate is the Principal.

Principal among these is clock / data misalignment, or clock skew.

The Principal Investigator for the mission is Dr. Dan McCammon of the University of Wisconsin.

To gain registration in the Principal Register or common law protection under the Lanham Act, a trade dress must not be “ functional .” That is, the configuration of shapes, designs, colors, or materials that make up the trade dress in question must not serve a utility or function outside of creating recognition in the consumer ’ s mind.

In Kenya the Attorney General is the Principal Legal Adviser to the Government and ex-officio Member of Parliament and Cabinet.

* November 19, 1969: Tomah, Wisconsin Principal Martin Mogensen is shot to death in his office by a 14-year-old boy armed with a 20 gauge shotgun.

He is voiced by Dan Castellaneta, and first appeared in the episode " Principal Charming ".

Later, Quimby briefly flees the city thinking his corruption has been exposed and is deemed to have " abandoned office " and is replaced by a short-lived " council of learned citizens " headed by Lisa Simpson, Professor Frink, Comic Book Guy, Lindsey Naegle, Dr. Hibbert, and Principal Skinner.