New posts in Dimension Theory Algebra

Equivalence of definitions of Krull dimension of a module

Converse of a dimension lemma

Krull dimension of $\mathbb{C}[x_1, x_2, x_3, x_4]/\left< x_1x_3-x_2^2,x_2 x_4-x_3^2,x_1x_4-x_2 x_3\right>$

Is $\operatorname{height} \mathfrak{p} + \dim A / \mathfrak{p} = \dim A$ true?