Etymology
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Iowa 

organized as a U.S. territory 1838; admitted as a state 1846, named for the river, ultimately from the name of the native people, of the Chiwere branch of the Siouan family; said to be from Dakota ayuxba "sleepy ones," or from an Algonquian language (Bright cites Miami/Illinois /aayohoowia/). On a French map of 1673 it appears as Ouaouiatonon. John Quincy Adams, in his diary entries on the House of Representatives debate on the territorial bill in 1838, writes it Ioway. Related: Iowan.

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Montana 

U.S. state, from Latinized form of Spanish montaña "mountain" (used in South America specifically of the forested region on the eastern slopes of the Andes), from Latin mont-, stem of mons (see mountain). The territorial name was proposed in 1864 by U.S. Rep. James H. Ashley of Ohio when it was created from Nebraska Territory, in reference to the Rocky Mountains, which however traverse only one end of it. Admitted as a state in 1889. Related: Montanan.

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Idaho 
1861 as a place name, originally applied by U.S. Congress to a proposed territorial division centered in what is now eastern Colorado; said at the time to mean "Gem of the Mountains" but probably rather from Kiowa-Apache (Athabaskan) idaahe "enemy," a name applied by them to the Comanches. Modern Idaho was organized 1861 as a county in Washington Territory; in 1863 became a territory in its own right and it was admitted as a state in 1890.
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empire (n.)

mid-14c., "territory subject to an emperor's rule;" in general "realm, dominion;" late 14c. as "authority of an emperor, supreme power in governing; imperial power," in Middle English generally of the Roman Empire.

From Old French empire "rule, authority, kingdom, imperial rule" (11c.), from Latin imperium "a rule, a command; authority, control, power; supreme power, sole dominion; military authority; a dominion, realm," from imperare "to command," from assimilated form of in- "in" (from PIE root *en "in") + parare "to order, prepare" (from PIE root *pere- (1) "to produce, procure").

Not etymologically restricted to "territory ruled by an emperor," but used that way. The Empire, meaning "the British Empire," first recorded 1772 (it officially devolved into "The Commonwealth" in 1931); before that it meant the Holy Roman Empire (1670s).

[P]roperly an empire is an aggregate of conquered, colonized, or confederated states, each with its own government subordinate or tributary to that of the empire as a whole. [Century Dictionary] 

Empire as the name of a style (especially in reference to a style of dresses with high waistlines) is by 1860, in reference to the affected classicism prevailing in France during the reign of Napoleon I (1804-15). Second Empire is in reference to the rule of Napoleon III of France (1852-70). New York has been called the Empire State since 1834.

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domination (n.)

late 14c., dominacioun, "rule, control by means of superior ability, influences, resources, or position; the exercise of power in ruling," from Old French dominacion "domination, rule, power" (12c.) and directly from Latin dominationem (nominative dominatio), noun of action from past-participle stem of dominari "to rule, have dominion over," from dominus "lord, master," literally "master of the house," from domus "house, home" (from PIE root *dem- "house, household") + -nus, suffix denoting ownership or relation. Sexual bondage sense is by 1961.

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sultan (n.)

1550s, from French sultan "ruler of Turkey" (16c.), ultimately from Arabic (Semitic) sultan "ruler, prince, monarch, king, queen," originally "power, dominion." According to Klein's sources, this is from Aramaic shultana "power," from shelet "have power." Earlier English word was soldan, soudan (c. 1300), used indiscriminately of Muslim rulers and sovereigns, from Old French souldan, soudan, from Medieval Latin sultanus. Related: Sultanic.

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potentate (n.)

c. 1400, potentat, "a ruler, lord, prince, monarch; person who possesses independent power or sway," from Old French potentat and directly from Late Latin potentatus "a ruler," also "political power," from Latin potentatus "might, power, rule, dominion," from potentem (nominative potens) "powerful," from potis "powerful, able, capable; possible;" of persons, "better, preferable; chief, principal; strongest, foremost," from PIE root *poti- "powerful; lord." 

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might (n.)

"quality of being able, ability to do or act, power," Middle English might, from Old English miht, earlier mæht "bodily strength, power; authority, dominion, control; ability," from Proto-Germanic *makhti- (source also of Old Norse mattr, Old Frisian, Middle Dutch, Dutch macht, Old High German maht, German Macht, Gothic mahts), a Germanic suffixed form of the PIE root *magh- "to be able, have power."

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interregnum (n.)
1580s, from Latin interregnum "an interval between two reigns," literally "between-reign," from inter "between" (see inter-) + regnum "kingship, dominion, rule, realm," related to regere "to rule, to direct, keep straight, guide" (from PIE root *reg- "move in a straight line," with derivatives meaning "to direct in a straight line," thus "to lead, rule"). In the republic, it meant a vacancy in the consulate. The earlier English noun was interreign (1530s), from French interrègne (14c.).
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condominium (n.)

1714, "joint rule or sovereignty, ownership exclusive of all except the co-owners," from Modern Latin condominium "joint sovereignty," apparently coined in German c. 1700 from Latin com "with, together" (see com-) + dominium "right of ownership, property, dominion," from dominus "lord, master, owner," from domus "house" (from PIE root *dem- "house, household").

A word in politics and international law until sense of "privately owned apartment" arose in American English 1962 as a special use of the legal term.

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