Monday 30 April 2018

Linguistic Focus 1 Endomorphism d・d = 0



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

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