Check that the union of a countable collection of o-fields Bj, j 2 1 need not be a o-field even if B; C B;+1. Is a countable union of o-fields whether monotone or not a field? Hint: Try setting 2 equal to the set of positive integers and let C; be all subsets of {1, ..., j} and B; = o (Cj). If Bi, i = 1,2 are two o-fields, B1 U B2 need not be a field. %3D

Check that the union of a countable collection of o-fields Bj, j 2 1 need not be a o-field even if B; C B;+1. Is a countable union of o-fields whether monotone or not a field? Hint: Try setting 2 equal to the set of positive integers and let C; be all subsets of {1, ..., j} and B; = o (Cj). If Bi, i = 1,2 are two o-fields, B1 U B2 need not be a field. %3D

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 14E: 14. a. If is an ordered integral domain, prove that each element in the quotient field of ...

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