Abstract
The study of generalized deviations of a partially ordered set has its roots in the study of the Krull dimension of rings and modules. The concept of Krull dimension for commutative rings was developed by E. Noether and W. Krull in the 1920s. In 1923 E. Noether [27] explored the relationship between chains of prime ideals and dimensions of algebraic varieties. After five years, W. Krull [23] developed her idea into a powerful tool for arbitrary commutative rings satisfying the ascending chain condition for ideals. These rings are known today as Noetherian rings. Later, algebraists gave the name (classical) Krull dimension to the supremum of the length of finite chains of prime ideals in a ring.
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