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Perth Amboy, New Jersey

Perth Amboy is a city in Middlesex County, New Jersey, United States. The City of Perth Amboy is part of the New York metropolitan area; as of the 2010 United States Census, the city's population was 50,814, reflecting an increase of 3,511 from the 47,303 counted in the 2000 Census, which had in turn increased by 5,336 from the 41,967 counted in the 1990 Census. Perth Amboy has a Hispanic majority population. In the 2010 census, persons of "Hispanic, Latino or Spanish origin" made up 78.1% of the population, the second-highest in the state, behind Union City at 84.7%. Perth Amboy is known as the "City by the Bay"; the earliest residents of the area were the Lenape Native Americans, who called the point on which the city lies "Ompoge". Perth Amboy was settled in 1683 by Scottish colonists and was called "New Perth" after James Drummond, 4th Earl of Perth. Perth Amboy was formed by Royal charter in 1718, the New Jersey Legislature reaffirmed its status in 1784, after independence; the city was a capital of the Province of New Jersey from 1686 to 1776.

During the mid-1800s, the Industrial Revolution and immigration grew the city, developing a variety of neighborhoods which residents from a diverse range of ethnicities lived in. The city developed into a resort town for the Raritan Bayshore near it, but the city has grown in other industries since its redevelopment starting from the 1990s. Perth Amboy features a historic waterfront; the Perth Amboy Ferry Slip was once an important ferry slip in the area, it was added to the National Register of Historic Places in 1978. The Raritan Yacht Club, one of the oldest yacht clubs in the United States, is located in the city. Perth Amboy is connected to the Staten Island borough of New York City via the Outerbridge Crossing; the Lenape Native Americans called the point on which the city is built "Ompoge", meaning "level ground" or "standing or upright". When settled in 1684, the new city was dubbed "New Perth" in honor of James Drummond, Earl of Perth, one of the 12 associates of a company of Scottish proprietors.

The Algonquian language name persisted, corrupted to Ambo, or Point Amboy, a combination of the native and colonial names emerged appearing in South Amboy. Perth Amboy was settled by Scottish colonists around 1683, recruited to inhabit the share of the East Jersey colony owned by Robert Barclay, a Quaker who would become the absentee governor of the province. Perth Amboy was formed by Royal charter on August 4, 1718, within various townships and again by New Jersey Legislature on December 21, 1784, within Perth Amboy Township and from part of Woodbridge Township. Perth Amboy Township was formed on October 31, 1693, was enlarged during the 1720s to encompass Perth Amboy city. Perth Amboy Township was incorporated as one of New Jersey's initial 104 townships through the Township Act of 1798 on February 21, 1798; the township was replaced by Perth Amboy city on April 8, 1844. Elizabeth was designated in 1668 as the first capital of New Jersey. In 1686, Perth Amboy was designated as the capital of East Jersey, while Burlington was the capital of West Jersey.

After the two were united as a royal colony in 1702, the two cities alternated as the capital of the Province of New Jersey until November 1790, when Trenton was designated as the unified state capital, chosen based on its location midway between New York City and Philadelphia. A few of the buildings from this early period can still be seen today. Most notably, the Proprietary House, the home of William Franklin, the last Royal Governor of New Jersey and estranged son of Benjamin Franklin, still stands in the waterfront area of the city. Architect John Edward Pryor was hired in 1761 to design and construct the building, completed in September 1764, years late and over budget. Franklin preferred his alternate home in Burlington. Franklin moved in 1774 into the Proprietary House. Franklin's father, tried unsuccessfully to convince his son to support the Colonial cause. William Franklin was arrested and detained at Proprietary House in 1776 until he was tried and convicted of treason. Perth Amboy City Hall was first built as a court house for Middlesex County in 1714, having been designated as the county seat the previous year.

The building was used as the home of the East Jersey Provincial Assembly. The building was destroyed by a major fire in 1731 and rebuilt in 1745. Another fire was deliberately set in 1764, forcing a rebuilding, completed in 1767, it is the oldest city hall in continuous use in the United States. On November 20, 1789, City Hall was the site where the New Jersey General Assembly met to ratify the Bill of Rights, becoming the first stae in the nation to do so. Market Square, located across from City Hall, is a park, an outdoor marketplace during the Colonial era. Market Square includes a replica of the Liberty Bell, a statue of George Washington and the Bill of Rights Arch, which commemorates the fact that New Jersey was the first state to ratify the Bill of Rights. St. Peter's Church, which held its first service in 1685 and received a royal charter in 1718, has been recognized as the first Episcopal congregation in the state, its current building, dating from the 1850s, is surrounded by a graveyard of early inhabitants and displays a collection of stained-glass windows with religious scenes as well as early depictions of New Jersey receiving her charter and a meeting between William Franklin and his father, Ben.

The Kearny Cottage is a remaining example of 18th-century vernacular architecture. Operated as a histori

Best Female Soccer Player ESPY Award

The Best Female Soccer Player ESPY Award was presented annually between 2002 and 2004 to the female soccer player adjudged to be the best in a given calendar year among those contesting the sport on the professional or international level. The award—and the Best Male Soccer Player ESPY Award—evolved from the Best Soccer Player ESPY Award, awarded in 2000 and 2001, the latter once more absorbed the gender-specific awards in 2005. During the award's three years, the voting panel comprised variously fans, who participated through Internet balloting; the ESPY Awards ceremony was conducted in June and awards conferred reflected performance and achievement over the twelve months previous to presentation. List of sports awards honoring women FIFA Women's World Cup Awards FIFA World Player of the Year Enumeration of past winners from HickokSports.com at the Library of Congress Web Archives 2004 ESPY Award winners 2003 ESPY Award winners 2002 ESPY Award winners

Dedekind domain

In abstract algebra, a Dedekind domain or Dedekind ring, named after Richard Dedekind, is an integral domain in which every nonzero proper ideal factors into a product of prime ideals. It can be shown that such a factorization is necessarily unique up to the order of the factors. There are at least three other characterizations of Dedekind domains that are sometimes taken as the definition: see below. A field is a commutative ring in which there are no nontrivial proper ideals, so that any field is a Dedekind domain, however in a rather vacuous way; some authors add the requirement. Many more authors state theorems for Dedekind domains with the implicit proviso that they may require trivial modifications for the case of fields. An immediate consequence of the definition is that every principal ideal domain is a Dedekind domain. In fact a Dedekind domain is a unique factorization domain if and only if it is a PID. In the 19th century it became a common technique to gain insight into integral solutions of polynomial equations using rings of algebraic numbers of higher degree.

For instance, fix a positive integer m. In the attempt to determine which integers are represented by the quadratic form x 2 + m y 2, it is natural to factor the quadratic form into, the factorization taking place in the ring of integers of the quadratic field Q. For a positive integer n the polynomial z n − y n can be factored over the ring Z, where ζ n is a primitive n root of unity. For a few small values of m and n these rings of algebraic integers are PIDs, this can be seen as an explanation of the classical successes of Fermat and Euler. By this time a procedure for determining whether the ring of all algebraic integers of a given quadratic field Q is a PID was well known to the quadratic form theorists. Gauss had looked at the case of imaginary quadratic fields: he found nine values of D < 0 for which the ring of integers is a PID and conjectured that there are no further values. However, this was understood in the language of equivalence classes of quadratic forms, so that in particular the analogy between quadratic forms and the Fermat equation seems not to have been perceived.

In 1847 Gabriel Lamé announced a solution of Fermat's Last Theorem for all n > 2, i.e. that the Fermat equation has no solutions in nonzero integers, but it turned out that his solution hinged on the assumption that the cyclotomic ring Z is a UFD. Ernst Kummer had shown three years before that this was not the case for n = 23. At the same time, Kummer developed powerful new methods to prove Fermat's Last Theorem at least for a large class of prime exponents n using what we now recognize as the fact that the ring Z is a Dedekind domain. In fact Kummer worked not with ideals but with "ideal numbers", the modern definition of an ideal was given by Dedekind. By the 20th century and number theorists had come to realize that the condition of being a PID is rather delicate, whereas the condition of being a Dedekind domain is quite robust. For instance the ring of ordinary integers is a PID, but as seen above the ring O K of algebraic integers in a number field K need not be a PID. In fact, although Gauss conjectured that there are infinitely many primes p such that the ring of integers of Q is a PID, as of 2016 we do not know whether there are infinitely many number fields K such that O K is a PID!

On the other hand, the ring of integers in a