let FCL fields, suppose that a 0 is algebraic over L. show that a- is algebraic...

 

Transcribed Image Text:

let FCL fields, suppose that a 0 is algebraic over L. show that a- is algebraic over L, it is assumed that a F b) suppose that a is algebraic over L and that a L. Show that a + a is algebraic over L c) Find the minimal polynomial of a + a d) show that a + a and a have the same degree over L. e) If a and are algebraic, it is a + algebraic f) what is the minimal polynomial? Let X be a set and let S be a collection of subsets of X. The algebra of subsets of X generated by S is always strictly smaller than the o-algebra of subsets of X generated by S. (In other words, the latter always contains more subsets of X than the former.) O True O False For a set X, let S be a collection of subsets of X and let A(S) be the o-algebra of subsets of X generated by S. If A' is an algebra of subsets of X satisfying SCA'CA(S), then the algebra A' is actually a o-algebra of subsets of X. True O False Let X be a set. Every algebra of subsets of X is also a o-algebra of subsets of X. O False o True For a set X, let S be a collection of subsets of X and let A(S) be the algebra of subsets of X generated by S. If A' is a o-algebra of subsets of X satisfying SCA'CA(S), then the algebra A(S) is actually a o-algebra of subsets of X. let FCL fields, suppose that a 0 is algebraic over L. show that a- is algebraic over L, it is assumed that a F b) suppose that a is algebraic over L and that a L. Show that a + a is algebraic over L c) Find the minimal polynomial of a + a d) show that a + a and a have the same degree over L. e) If a and are algebraic, it is a + algebraic f) what is the minimal polynomial? Let X be a set and let S be a collection of subsets of X. The algebra of subsets of X generated by S is always strictly smaller than the o-algebra of subsets of X generated by S. (In other words, the latter always contains more subsets of X than the former.) O True O False For a set X, let S be a collection of subsets of X and let A(S) be the o-algebra of subsets of X generated by S. If A' is an algebra of subsets of X satisfying SCA'CA(S), then the algebra A' is actually a o-algebra of subsets of X. True O False Let X be a set. Every algebra of subsets of X is also a o-algebra of subsets of X. O False o True For a set X, let S be a collection of subsets of X and let A(S) be the algebra of subsets of X generated by S. If A' is a o-algebra of subsets of X satisfying SCA'CA(S), then the algebra A(S) is actually a o-algebra of subsets of X.