Linguistic Focus 1 Endomorphism d・d = 0 / August 19, 2007

Linguistic Focus

1

Endomorphism   d・d = 0

　　  TANAKA Akio

1

Assumption is given by the following.

Additive group M has endomorphism d that satisfies d・d = 0.

d-additive group    ( M, d )

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 D^i,j     ( i, j ) ∈ Z²

On commutative table of D^i,j ,horizontal, vertical and diagonal sequences has d・d = 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.

d・d = 0 is connection rule.

Tokyo August 19, 2007

Sekinan Research Field of Language