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In order-theoretic mathematics, the **deviation of a poset** is an ordinal number measuring the complexity of a partially ordered set.

The deviation of a poset is used to define the Krull dimension of a module over a ring as the deviation of its poset of submodules.

A poset is said to have deviation at most α (for an ordinal α) if for every descending chain of elements *a*_{0} > *a*_{1} >... all but a finite number of the posets of elements between *a*_{n} and *a*_{n+1} have deviation less than α. The deviation (if it exists) is the minimum value of α for which this is true.

Not every poset has a deviation. The following conditions on a poset are equivalent:

The poset of positive integers has deviation 0: every descending chain is finite, so the defining condition for deviation is vacuously true. However, its opposite poset has deviation 1.

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Deviation_of_a_poset

**Deviation** may refer to:

- Standard deviation, which is based on the square of the difference
- Absolute deviation, where the absolute value of the difference is used
- Relative standard deviation, in probability theory and statistics is the absolute value of the coefficient of variation

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Deviation

The doctrine of **deviation** is a particular aspect of contracts of carriage of goods by sea. A deviation is a departure from the "agreed route" or the "usual route", and it can amount to a serious a breach of contract. The consequences of unjustified deviation are very grave for the carrier, who is thereby prevented from relying upon any exclusion clause which limits his liability.

The "agreed route" is identified from the contract of carriage, as evidenced by the bill of lading. The ports of origin and destination (e.g. "Piraeus to Liverpool"') define the route. The "usual route" is not necessarily the shortest route, but is a version of the agreed route, taking into account safety issues, distances, seasonal conditions and war zones. For instance, the route "Auckland to London" could be via Suez, Panama, the Cape of Good Hope, or Cape Horn, but the usual route will be identified by reference to current practice or to any previous dealings of the parties.

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Deviation_(law)

* Deviation* is an album by American banjoist Béla Fleck, released in 1984. It was recorded with the second classic line-up of the New Grass Revival, consisting of Béla Fleck, Sam Bush, John Cowan and Pat Flynn.

All tunes written by Béla Fleck, except where noted.

Special Guests:

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Deviation_(Béla_Fleck_album)

In mathematics, especially order theory, a **partially ordered set** (or **poset**) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a binary relation that indicates that, for certain pairs of elements in the set, one of the elements precedes the other. Such a relation is called a *partial order* to reflect the fact that not every pair of elements need be related: for some pairs, it may be that neither element precedes the other in the poset.
Thus, partial orders generalize the more familiar total orders, in which every pair is related. A finite poset can be visualized through its Hasse diagram, which depicts the ordering relation.

A familiar real-life example of a partially ordered set is a collection of people ordered by genealogical descendancy. Some pairs of people bear the descendant-ancestor relationship, but other pairs bear no such relationship.

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Partially_ordered_set

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