Question

IBMISSION Аа Let R be a ring and let I be an ideal of R. Recall the canonical map T: RR/I given by *(r) = r + I is a ring homomorphism from R to R/I that is onto R/I, but not one-to-one. Let S be a subring of R where I SS. Part 1: Explain why +(S) is a subring of R/I. (Hint: Don't make this difficult. Can you use the corollary in the previous video?)

$INSTRUCTIONS Make a conjecture about (Z_n, +, times) by filling in the following blank: The ring (Z_n, +, \times) is a field$

Answer 1

o R is ring where a, b E S ANSWER ring I ideel of R The canonual map T: RR horonarplainen r r + I, It is onte but not 1-1. Let S cR be any subring where Ics. CLAIM 8 - T (8) is subring off Firstly t we will check that T(s) is subgroup ie T (a)- T (6) I Ca- b) T. I is an ETICS) home - 7 [: 8 in subgroup classmate

DATE => T(S) is subgroup Now, take I (a), (6) ET (3) I Cad. (6) iT Cab) ETG) { abes 1. S is subring => T(S) & subzing of f. g) is field (20) 2) * element in 7 has every inverse <-> element is every co- frine en prime number