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\n Solve problem 5 which is on Abstract Algebra. Question is based on Quotient Rings.\n <\/p>\n

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• \n Attachment 1\n <\/li>\n
• \n Attachment 2\n <\/li>\n<\/ul>\n

  Problem 5. Suppose that R = (R, +,*) and S = (S, +,*) are rings, and suppose that f : R – S is a ringhomomorphism that is onto.Part (a). If a E R and x E a + ker(f), prove that f (x) = f (a).Part (b). If a, b E R are such that f (a) = f(b), prove that a – b E ker(f).Part (c). If a, b E R are such that f (a) = f(b), use Part (b) to prove that a + ker(f) = b + ker(f).Part (d). Define a function Of : LCker(\/) – S according to the rule of (a + ker(f)) = f (a). Prove thatOr is a bijection.Part (e). Prove that Or is a ring isormorphism.\n<\/p><\/div>\n","protected":false},"excerpt":{"rendered":"

  Solve problem 5 which is on Abstract Algebra. Question is based on Quotient Rings. Attachment 1 Attachment 2 Problem 5. Suppose that R = (R, +,*) and S = (S, +,*) are rings, and suppose that f : R – S is a ringhomomorphism that is onto.Part (a). If a E R and x E […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_joinchat":[]},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/posts\/228088"}],"collection":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/comments?post=228088"}],"version-history":[{"count":0,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/posts\/228088\/revisions"}],"wp:attachment":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/media?parent=228088"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/categories?post=228088"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/tags?post=228088"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}