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(a) Let R be a ring, a € R and define AR = {r € R | ar = OR} where OR ER is the zero element of R. Then check as to whether AR is a subring of R. or not (b) Let R be a ring and S be a subring of R. and show that OR = 0s, where OR, Os are the zero elements in R, S respectively

(a) Let R be a ring, a € R and define AR = {r € R | ar = OR} where OR ER is the zero element of R. Then check as to whether AR is a subring of R. or not (b) Let R be a ring and S be a subring of R. and show that OR = 0s, where OR, Os are the zero elements in R, S respectively

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a) Let R be a ring, a € R and define AR = {r € R | ar = OR} where OR ER is the zero element of R. Then check as to whether AR is a subring of R. or not (b) Let R be a ring and S be a subring of R. and show that OR = 0s, where OR, Os are the zero elements in R, S respectively
Transcribed Image Text:(a) Let R be a ring, a € R and define AR = {r € R | ar = OR} where OR ER is the zero element of R. Then check as to whether AR is a subring of R. or not (b) Let R be a ring and S be a subring of R. and show that OR = 0s, where OR, Os are the zero elements in R, S respectively
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