Form Classes

Statement:

Let \(R\) be a commutative ring with identity, \(B\) a proper subring containing 1 and \(q\) a prime ideal in \(B\). Then there is a subring \(A\) of \(R\) and a prime ideal \(p\) in \(A\) such that

  1. \(B\subseteq A\)
  2. \(q = B\cap p\)
  3. \(R - p\) is multiplicatively closed and
  4. if \(A\neq R\),
then \(R - A\) is multiplicatively closed.

Howard_Rubin_Number: 226

Parameter(s): This form does not depend on parameters

This form's transferability is: Unknown

This form's negation transferability is: Negation Transferable

Article Citations:
Rav-1977: Variants of Rado's selection lemma and their applications

Book references

Note connections:

The following forms are listed as conclusions of this form class in rfb1:

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