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 Di,j ( i, j ) ∈ Z2
On commutative table of Di,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
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