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Which of Examples 1 through 5 are fieldsReference:EXAMPLE

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

Solution for problem 2E Chapter 13

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 2E

Problem 2E

Which of Examples 1 through 5 are fields?


EXAMPLE 1 The ring of integers is an integral domain

EXAMPLE 2 The ring of Gaussian integers Z[i] = {a + bi | a, b Z} is an integral domain.

EXAMPLE 3 The ring Z[x] of polynomials with integer coefficients is an integral domain.

EXAMPLE 4 The ring is an integral domain.

EXAMPLE 5 The ring Zp of integers modulo a prime p is an integral domain.

Step-by-Step Solution:
Step 1 of 3

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FEMA, DOD, DOE, EPA, HHS Intelligence Collection • Although many places could be targets that terrorist choose to attack, it is impossiblefor the federal governmentand state and local governments to provide security for every potential target • Key distinction: FBI=Domestic intelligencecollection, CIA=foreignintelligencecollection • The 9/11 Commission Report criticized the government's intelligence sharing practices and concluded that this resulted in a failure to "connect the dots"' • Federal Agencies and Anti-terrorism ○ Joint Terrorism Task Force (JTTF): an FBI sponsored group comprised of federal, state and local law enforcement officials brought together to address specific threats Notes Page 1 together to address specific threats ○ Located in each of the FBI's 56 field offices throughout the United States ○ In addition to local JTTF branches, there is also a national JTTF located in Washington, DC which includes personnel from the following departments/agencies:  DOE, DOD, Federal Emergency ManagementAgency (FEMA), CIA,US Customs and Border Protection, US Immigration and Customs Enforcement, US Secret Service • Fusion Centers ○ Established by state and local law enforcement agencies ○ Serve as intelligenceoperations centers for both homeland security and crime related matters • Law Enforcement Intelligence Units ○ Generally,local and state law enforcement agencies may only gather information on citizens when reasonable suspicion or probable cause exists ○ NYPD's Demographic Unit (disbanded in 2014) was one of the few that had gathered terrorist-related data  Ex. 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Reevaluation:reanalysis of intelligenceproducts to determine their accuracy and effectiveness Espionage Act of 1917 • Originallymade it unlawful to interfere with any US war effort or to assist in the success of the nation's enemies • The followingyear, this legislationwas expanded upon by the Sedition Act which made it unlawful to do an increasing number of things considered to run counter to the US or our war efforts ○ Ex. Sedition Act of 1918 eventually repealed, but much of the Espionage Act remains in effect Foreign Intelligence SurveillanceAct of 1978 • Essentially, allows for the collection of electronic information when there is reason to suspect that the information is of national security interest (i.e. related to terrorism or espionage) ○ Ex. Orders are issued by the Foreign IntelligenceSurveillance Court (FISC) ○ Ex. Expanded several times since 1978 Expansion of Federal Power Post 9/11 (Enemy Combatant ) • Military order of November 2001 ○ Signed by PresidentGeorge W. 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No right to habeas corpus, confront witnesses or challenge evidence (particularly national security related) • USA Patriot Act ○ Enacted in October 2001 ○ Greatly expands the federal government's enforcement powers  Greater surveillance powers (authorized under Section 213 and 214 as well as the Foreign IntelligenceSurveillance Act), fewer civil rights for individualswith links to terrorism ○ Section 215: allows the FBI to seize records from a third party without probable cause when a national security purpose exists Local Issues Post 9/11 • Limited police resources and other issues ○ Local police departments encounter huge financial costs in response to terrorist attacks around the world  Ex. London Bus Bombing (July 2005) ○ Cities may resemblefortresses, which leads to traffic and tourism related issues ○ Police officers must also be paid overtime and provided with proper protective equipment Border Protection and Homeland Security • Sealing the borders ○ Largely the responsibilityof Homeland Security Investigations (HSI) 2 primary responsibilities: Notes Page 2 ○ 2 primary responsibilities: 1. Securing the borders and stopping illegalimmigration 2. Ensuring employers follow federal laws in verifying whether people can legallywork in the United States • Smart Passports ○ Passports containing microchips that can be scanned electronically and contain a large amount of information about the carrier  Ex. DOB, photograph, iris scans, digital fingerprints, etc. • Passenger screening and No-Fly list ○ Passenger screening is the primary responsibility of the TSA ○ No-Fly list is maintained by the Terrorist Screening Center (TSC)  Primary concern: it is unknown exactly how names end up on the list • National Identification Cards ○ Although no uniform national identification card has been created and issued in the US, the REAL ID Act of 2005 sets standards for the issuance of various sources of identification, such as state driver's licenses  Ex. Illinois,Minnesota, Missouri, and Washington still completely non-compliant Civil Rights Issues and Homeland Security • Free Speech ○ Typically, part of free speech is the freedom to provide support to various organizations ○ However, federal antiterrorism laws prohibit providing any form of material support to terrorist organizations • Racial Profiling ○ One concern is the indiscriminate arrest of Muslims without probable causes and abuse of the "material witness law" ○ Public opinion generallydoes not support racial profiling,however the profiling of Muslims remains a key concern post 9/11 • Rendition, Torture and the Killingof US citizens ○ Rendition: transfer of enemy combatant to another country where their due process rights are greatly diminished  Largely supported by the Bush Administration after 9/11 but scaled back by the Obama Administration ○ Killingof US citizens  Notably, Anwar al-Awlaki,who was killedin a 2011 drone strike in Yemen Notes Page 3

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Chapter 13, Problem 2E is Solved
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Textbook: Contemporary Abstract Algebra
Edition: 8
Author: Joseph Gallian
ISBN: 9781133599708

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Which of Examples 1 through 5 are fieldsReference:EXAMPLE