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2. Let S be a collection of sets. Show that there exist a unique o-ring R(S) such that 1. SC R(S). 2. If Ř is a o-ring with SCR, then R(S) C R. (b) Show that, for S = closed sets. {(a,b) | a,b ≤ R, a < b}, the o-ring R(S) contains all open and

2. Let S be a collection of sets. Show that there exist a unique o-ring R(S) such that 1. SC R(S). 2. If Ř is a o-ring with SCR, then R(S) C R. (b) Show that, for S = closed sets. {(a,b) | a,b ≤ R, a < b}, the o-ring R(S) contains all open and

Elements Of Modern Algebra
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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2. Let S be a collection of sets. Show that there exist a unique o-ring R(S) such that 1. SC R(S). 2. If Ř is a o-ring with S C Ř, then R(S) C Ř. (b) Show that, for S = {(a,b) | a,b R, a < b}, the o-ring R(S) contains all open and closed sets.
Transcribed Image Text:2. Let S be a collection of sets. Show that there exist a unique o-ring R(S) such that 1. SC R(S). 2. If Ř is a o-ring with S C Ř, then R(S) C Ř. (b) Show that, for S = {(a,b) | a,b R, a < b}, the o-ring R(S) contains all open and closed sets.
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