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is then an area ring with the maximal excellent p R p displaystyle mathfrak p R_ mathfrak p
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are each of the identities and R k → R j → R i displaystyle R_ k to R_ j to R_ i
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as a direct sum of abelian teams (because for abelian groups finite solutions are the same as direct sums). Plainly the immediate sum of this kind of ideals also defines a product of rings that is isomorphic to R.
For commutative rings, the ideals generalize the classical Idea of divisibility and decomposition of the integer into prime numbers in algebra. A correct best P of R is termed a main great if for just about any factors x , y ∈ R displaystyle x,yin R
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For virtually any ring link R, you will discover a unique ring homomorphism Z → R plus a unique ring homomorphism go R → 0.