For the Supposition of KARCEVSKIJ Sergej
Meaning Minimum of Language
October 5, 2011
[Preparation]

,
is graded ring and integral domain.
For negative
e,

.
R's quotient field element is called homogenious when
R's quotient field element is ratio
f/g of homogenious element

.
Its degree is defined by

.
<Definition>
At R's quotient field, subfield made by degree 0's whole homogenious elements,

,
is expressed by

.
For homogenious element

,
subring of field

,

,
is expressed by

.
For graded ring,

,
algebraic variety that

is quotient field that whole

for homogenious element

is gotten by gluing in common quotient field

is expressed by Proj
R.
Proj R of graded ring

,
,is called projective algebraic variety.
<Composition>
Projective algebraic variety is complete.
◊
<System>
Moduli of hypersurface,

,
is complete algebraic variety.
◊

,
is sum set of,

,

.
◊
[Interpretation]
Word is expressed by,

.
Meaning minimum of word is expressed by,

,

.
For meaning minimum,
refer to the next.
[References]
This paper has been published by Sekinan Research Field of Language.
Tokyo