Theorem

Krull dimension of an infinite product

In an infinite product of rings, if infinitely many of the rings have positive dimension, then the product ring has infinite dimension.

Link: https://www.ams.org/journals/tran/1992-331-02/S0002-9947-1992-1041047-4/S0002-9947-1992-1041047-4.pdf

Reference(s)

  • R. W. Gilmer and W. Heinzer. Products of commutative rings and zero-dimensionality. (1992) @ Proposition 3.3 p 667