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Suppose that n1, n2, . . . , nk are positive even

Contemporary Abstract Algebra | 8th Edition | ISBN: 9781133599708 | Authors: Joseph Gallian ISBN: 9781133599708 52

Solution for problem 51E Chapter 8

Contemporary Abstract Algebra | 8th Edition

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Contemporary Abstract Algebra | 8th Edition | ISBN: 9781133599708 | Authors: Joseph Gallian

Contemporary Abstract Algebra | 8th Edition

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Problem 51E

Suppose that n1, n2, . . . , nk are positive even integers. How many elements of order 2 does Zn1 ? Zn2 ? . . . ? Znk have ? How many are there if we drop the requirement that n1, n2, . . . , nk must be even?

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Study Guide for Global Studies final Politics: the process through which people make decisions (whose view will be and what method will be adopted(POWER)). Issues of Power: Political Science about how politics will affect people ad the goverment at level and power. State: Political entity that: 1) claims allegiance of a given population, 2) exercises a monopoly of violence or legitimate use of coercive force, 3) controls a territory inhabited by citizens and or subjects , and 4) has sovereignty Sovereignty: independent and has the ability to use force andassert power. Nation: a distinct group of people of common cultural background (Religion, ethnic, historical, geographical, language, ect.) Ex Nation of Islam Nation-state: Political entity (state) associated with a particular cultural entity (nation) State-less nation: Nations that share a common identity but do not have a homeland (Kurdish is an example) Nationalism: what should bind nation/ people to the state; tendency to view one's country as superior to others (patriotism) Treaty of Westphalia: created in 1648 at the end of the Protestant Reformation (for which religion could be praticed anywhere through absolute sovereignty) formed the borders of European states. Juridicial Statehood: refers to the legal right of sovereignty and control over territory. Empirical Statehood: a capacity for internal cohesiveness,effective control and civil governement *The United Nations* Non-Governmental Organization(NGO): international organization that does not work for the government (created by anybody for any cause) ex. Amnesty International Interngovernmental Organization (IGO):Organization ran by multiple governments (3 or more nation-states, signed by treaties, have number of organs which are agencies within organizations, perform many functions)ex. EU (european union) Problems with this- -Anarchy:conflict of national interests,IGOs require broad-based consensus -Sovereignty: statesmay be reluctant to participate when sensitive topics are at stake (participation) -Collective Good: "free riding" impairs international policy success. "If they're going to take care of it, why should I help" League of nations: -after WW1, League of Nations was created to try to prevent another World War. Woodrow Wilson wanted to create the organization in 1919 with 14 points that could fix the problems, which were: 1)open covenance of peace(there shall be no private international understandings, 2)Absolute freedom of navigation , 3) The removal of all economic barriers and establishment of an equality of trade,4)National armaments will be reduced , 5)A free open-minded and absolutely impartial adjustment of colonial claims, 6) the evacuation of Russian territories, 7) Belgium must be evacuated and restored, 8)all French territory shouold be freed and the invaded portions restored, 9)a re-adjustment of the frontiers of Italy should be effected along clearly recognized lines of nationality, 10) the people of Austria-Hungary should be accorded the freest opportunity to autonomous development 11) Romania, Serbia, and Montenegro should be evacuated, occupied territories restored, 12)the Turkish portion of the Ottoman Empire should be assured a secure sovereignty,13)an independent Polish state should be create which should be include territories inhabited by indisputably Polish populations, and 14) a general association of nations must be formed under specific covenants for the purpose of affording mutual guarantees of political independence and territorial integrity. His idea did not work , the US did not even participate in the League of Nations After WW2: another IGO, The United Nations, was created in 1945 by 57 countries, to prevent another world war. The US participated this time (it's headquaters is located in Manhattan) There are currently 193 members,and south sudan recently was granted membership in 2011. They meet in a General Assembly, the closest thing to a world parliament. Principles of the UN -All member states have sovereign equality -All member states must obey the Charter -Countries must try to settle their differences by peaceful means -UN may not interfere in domestic affairs -Try to assist the other countries in the UN 4 Aimsof the UN -To keep peace throughout the world -Develop friendly relations between nations -Work together to help people live better lives, eliminate poverty, disease, and illiteracy. -Be a center for helping nations acheive these aims UN Council consists of 6 organs 1)Security Council 2)Secretariat 3) General Assembly 4) Economics and Social Concil (Human Rights) 5)Trusteeship Council(helped with decolonisation, is finished) 6) International Court of Justice -They are separate, autonomous IGO which work with the UN and with each other. Their work in a country or between countries is always carries out in partnership. General Assemby- operates like a town hall, the President of the General Assembly is elected by peers and serves for one year: meets Sep-Dec (3 months) -Decisions require 2/3 majority abd the Security Council must pass it Secretariat ); Executive Branch of the UN; carries out diverse day-to-day work of the organization and administers the programs and policies. Secretary-General: Ban ki Moon; appointed by the General Assembly for 5 year term Security council: Most Powerful body of the UN -Responsibility for the maintenance of international peace and security, must recommend admission of new Members -15 members and each has one vote -*The are 5 Permament Members: if one vetos, the resolution fails [10 other members serve 2 year term] 9 votes to pass a resolution, although all 5 permanent members must approve. (5 Members are: United States, France, Great Britian, China, and Russia) * Constraints on State Sovereignty: even if you don't want to be in the UN, you are, which constrains a state's ability to make decisions. The World Trade Organization (WTO) : An international organization designed to promote free and uniform trade and banking and finance rules and regulations. European Union- regional organization which linked economies together to benefit Peacekeeping: Originally involved monitoring crossfires and supervising truces between warring factions (during the Cold War).After the Cold War, became Humanitarian Interventionism (directed at 2 purposes: Emergency assistance and protecting fundamental human rights) Didn't do very many peacekeeping in the UN until the 80's because; 1)Cold War- States were more concerned in what was going on in their own states 2) No pressure from domestic public 3) Cold War politics and Super Power interests prevented UN security Council from passing any resolutions End of Cold War (between 1988-1993)- 20 mew peacekeeping missions were established Cold War Era- kepping peace between two consenting parties Post Cold War- protecting territory, people, and aid operations, disarming belligerents. * Consent was no longer required in cases to use force if necessary to protect civilians or disarm belligerents. 3 Failures in the UN 1) Srebrenica Massacre (1955)- War in Bosnia , Bosnian Serbian Army committed genocide against Bosnian Muslims who were located in UN designated "safe zone"- UN didn't help because they didn'tfire back. 2) Somalia(1991) - Under falling harsh conditions while the second civil war was underway, 1000's of civilians had died. UNO was sent in to establish secure safe-zones, UNOSOM 1; warlord cut off aid and US led strong 37000 task force. 1993 UNISOM II was 28000 strong,was given task by UNITAF that nothing less than the disarmament of the warring parties and successful reconstruction of Somalia. 3) Rwandan Genocide(1993-94) - In 100 days (Aprill-July) 800000 people were massacred . After being forced to allow Tutsi's to be included in government and exclude Hutu Extremists, the Hutu Extremist campaigned to slaughter Tutsi minority. The UN knew it would happen, yet did nothing. Intervention pessimism: little can be done without the consent of major parties involved Intervention optimism: the international community can forcibly rebuild failed states and reform muderous ones-even if consent must be induced. Cohen- The process of state-making 1)The expansion and or consolidation of borders (war) 2) The maintenance of order (policing) 3) Extraction of resources to maintain the apparatuses of the states (taxation) -Ayoob says: In order to have these, you must have a monopoly of violence( 1 of the three main points of a state definition).

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Chapter 8, Problem 51E is Solved
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Textbook: Contemporary Abstract Algebra
Edition: 8
Author: Joseph Gallian
ISBN: 9781133599708

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Suppose that n1, n2, . . . , nk are positive even