(a) Let R be a ring, a € R and define AR = {r € R|ar = ar = OR} where OR ER is the zero element of R. Then check as to whether AR is a subring of R or not

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.3: The Characteristic Of A Ring
Problem 22E: 22. Let be a ring with finite number of elements. Show that the characteristic of divides .
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(a) Let R be a ring, a € R and define
AR = {r € R|ar
=
ar = OR}
where OR ER is the zero element of R. Then check as to whether AR is a subring of R or not
Transcribed Image Text:(a) Let R be a ring, a € R and define AR = {r € R|ar = ar = OR} where OR ER is the zero element of R. Then check as to whether AR is a subring of R or not
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