Part b from #12 Thomas W. Hungerford - Abstrac x+O File | C:/Users/angel/Downloads/Thomas%20W.%20Hungerford%20-%20Abstract%20Algebra_%20AN%20lntroduction-Cengage%20Learning%20(201.....Flash Player will no longer be supported after December 2020.Turn offLearn moreof 621+-- A' Read aloudV DrawF HighlightO Erase89numbers is a subring of M(R).10. Let R and S be rings and consider these subsets of R X S:R= {(r, Os) |rER} and S= {(OR, s) | SES}.%3D(a) If R= Z3 and S = Zs. What are the sets R and S?(b) For any rings Rand S, show that Ris a subring of RX S.Goun at(c) For any rings R and S, show that S is a subring of RX S.11. Let R be a ring and ma fixed integer. Let S = {rɛR|mr =is a subring of R.OR}. Prove that S12. Let a and b be elements of a ring R.(a) Prove that the equation a + x = b has a unique solution in R. (Youmust prove that there is a solution and that this solution is the onlyone.)(b) If R is a ring with identity and a is a unit, prove that the equation ax = bhas a unique solution in R.13. Let Sand T be subrings of a ring R. In (a) and (b), if the answer is "yes,"prove it. If the answer is “no," give a counterexample.(a) Is Sn Ta subring of R?(b) Is SU Ta subring of R?Copyrigt 2012Ca ng AN Righ Ra nd May aot be apied ed ar dapticd is whele ar ta part D to dearonie cig, tird pary eate mey be ned fon te eBoak darehagerta). Bd N baned ttoy apped a d dly dea be ovd ing apria Cagge Loaing a eright to ove dddonnl a ty timef D dghts cetti nt9:06 AMO Search for anythingEPICAiEPICO 4)3412/7/2020

Name: Part b from #12 Thomas W. Hungerford - Abstrac x+O File | C:/Users/ang
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Description: Part b from #12 Thomas W. Hungerford - Abstrac x+O File | C:/Users/angel/Downloads/Thomas%20W.%20Hungerford%20-%20Abstract%20Algebra_%20AN%20lntroduction-Cengage%20Learning%20(201.....Flash Player will no longer be supported after December 2020.Turn