Saturday, 26 April 2025

Linguistic Focus 1 Endomorphism d・d = 0

 

Linguistic Focus

 

1

 

Endomorphism   dd = 0

 

 

    TANAKA Akio

 

1

Assumption is given by the following.

Additive group has endomorphism d that satisfies dd = 0.

d-additive group    ( Md )

Endomorphism of d-additive group    Abbreviated to d

Ker d     Z ( M )

Im d      B ( M )

From assumption    B ( M ) Z ( M )

Cohomology group of d-additive group M     residue additive group H ( M ) = Z ( M ) / B ( M )

 

2

Commutative ring    A

On double complex of A additive group D, assumption is given by the following.

A additive  group Di,    ( ij )  Z2

On commutative table of Di,,horizontal, vertical and diagonal sequences has dd = 0.

 

3

By double complex, the table has infinitive plane.

 

4

Commutative table made by double complex is identificated to language by comparison.

Commutative table is Language. The table’s infinity guarantees language’s infinity.

Double complex is word.

Endomorphism d is grammar.

dd = 0 is connection rule.

 

Tokyo August 19, 2007

Sekinan Research Field of Language

www.sekinan.org

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