Monday 5 January 2015

Linguistic Result From Cut and Glue Dimension to Krull Dimension 8th for KARCEVSKIJ Sergej / September 26, 2007

Linguistic Result

From Cut and Glue Dimension to Krull Dimension

8th for KARCEVSKIJ Sergej

    TANAKA Akio


Krull dimension of commutative ring is helpful to some concepts, i.e. <dimension by cut and glue>, <string and i-string>, <world and anti-world> and <true and false>.
Outline for reconstruction is roughly expressed by the next.
(1) Element of meaning on word is expressed by prime ideal.
(2) Word has dimension that is expressed by height of prime ideal’s maximum value.
(3) Word is expressed by Noetherian ring or Artinian ring.
(4) Sentence is expressed by exact sequence that contains direction of sentence which is expressed by covariant functor and Contravariant functor.
(5) Concept of string and i-string on sentence is connected with true and false in comparison with localization of commutative ring that contains algebraic set, Spec (A) and Zariski topology.
(6) Zariski topology satisfies axiomatic system of closed set.
(7) Axiom of choice is considered from the root of the theory for word and sentence.

[References]
Tube-Ring Theory   Freedom and String   Structures of Multi Dimensional Spaces     Hinoemata July 16, 2006
Tube-Ring Theory   True and False   Hierarchy of Language     Tokyo July 25-28, 2006
[Reference premise]
Algebraic Linguistics   Premise of Algebraic Linguistics 3-4     Tokyo September 24, 2007      

Tokyo September 26, 2007
Sekinan Research Field of Language

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