Higher Algebra (2 Volumes) by Helmut Hasse By Helmut Hasse

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Additional resources for Higher Algebra (2 Volumes)

Example text

It will be designated by K(xl"'" xn), its elf'ments by

Similarly deSignated. fact of the existence of the equation, we will introduce a special symbol ~ (contrariwise, =/=) to designate conditional equality. "", XJI)' 1. I. Rings, Fields, Integral Domains 54 First by applying the principle of substitution to the relation cp - cp' =1jJ the equation cp(Xl' ••. , xn)~

XI']' then a function value can be associated according to Dei. Lg for at least one system of elements Xl" •• , XII in K. ()n the basis of Theorem 13 the remarks about I [Xl' ... , XII J made in connection with Theorem 12 may accordingly be 5. Formulation 01 the Basic Problem of Algebra 53 applied to K(x 1, · · . , X n), too. Hence our notational lonYemilln shall also be yalid for the elements of K(x 1••••••1',,), 5. Detailed Formulation of the Basic Problem of Algebra By llleans of the concepts explamed in the preceding.