Traducción y análisis de palabras por inteligencia artificial ChatGPT
En esta página puede obtener un análisis detallado de una palabra o frase, producido utilizando la mejor tecnología de inteligencia artificial hasta la fecha:
- cómo se usa la palabra
- frecuencia de uso
- se utiliza con más frecuencia en el habla oral o escrita
- opciones de traducción
- ejemplos de uso (varias frases con traducción)
- etimología
join-irreducible - traducción al ruso
!['''Pic. 7:''' Non-lattice poset: <math>b</math> and <math>c</math> have common upper bounds <math>d, e,</math> and <math>f,</math> but none of them is the [[least upper bound]].](https://commons.wikimedia.org/wiki/Special:FilePath/NoLatticeDiagram.svg?width=200 "'''Pic. 7:''' Non-lattice poset: <math>b</math> and <math>c</math> have common upper bounds <math>d, e,</math> and <math>f,</math> but none of them is the [[least upper bound]].")
!['''Pic. 8:''' Non-lattice poset: <math>a</math> and <math>b</math> have common lower bounds <math>0, d, g, h,</math> and <math>i,</math> but none of them is the [[greatest lower bound]].](https://commons.wikimedia.org/wiki/Special:FilePath/Pow3nonlattice.svg?width=200 "'''Pic. 8:''' Non-lattice poset: <math>a</math> and <math>b</math> have common lower bounds <math>0, d, g, h,</math> and <math>i,</math> but none of them is the [[greatest lower bound]].")
!['''Pic. 1:''' Subsets of \{x, y, z\}, under [[set inclusion]]. The name "lattice" is suggested by the form of the [[Hasse diagram]] depicting it.](https://commons.wikimedia.org/wiki/Special:FilePath/Hasse diagram of powerset of 3.svg?width=200 "'''Pic. 1:''' Subsets of \{x, y, z\}, under [[set inclusion]]. The name \"lattice\" is suggested by the form of the [[Hasse diagram]] depicting it.")
![partition]]s of \{1, 2, 3, 4\}, ordered by "''refines''".](https://commons.wikimedia.org/wiki/Special:FilePath/Lattice of partitions of an order 4 set.svg?width=200 "partition]]s of \{1, 2, 3, 4\}, ordered by \"''refines''\".")
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Wikipedia
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet). An example is given by the power set of a set, partially ordered by inclusion, for which the supremum is the union and the infimum is the intersection. Another example is given by the natural numbers, partially ordered by divisibility, for which the supremum is the least common multiple and the infimum is the greatest common divisor.
Lattices can also be characterized as algebraic structures satisfying certain axiomatic identities. Since the two definitions are equivalent, lattice theory draws on both order theory and universal algebra. Semilattices include lattices, which in turn include Heyting and Boolean algebras. These lattice-like structures all admit order-theoretic as well as algebraic descriptions.
The sub-field of abstract algebra that studies lattices is called lattice theory.
