Prove for R a commutative ring with unity, R is a Noetherian ri... | Filo
Prove for R a commutative ring with unity, R is a Noetherian ri... | Filo
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SOLVED:Let R be a commutative ring with identity of prime characteristic p. If a, b ∈R and n ≥1, prove that (a-b)^p^'=a^p^'-b^p^'.
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SOLVED:Let R be a commutative ring with unit element. A nonempty subset S of R is called a multiplicative system if: (1) 0 ∈S. (2) s1, s2 ∈S implies that 81 s2 ∈S. Let 9 πbe the set of all ordered pairs (r, s) where r ∈R, s ∈S . In 9 πdefine (r, s) ∼(r^', s^') if there exists an element s^'' ∈S such that g^''(r 8^'-8 r^')=0 . (a) Prove that this defines an equivalence relation on 9 π. Let the equivalence class of (r, s) be denoted by [r, 8], and let RS be the set of all the equivalence classes.
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