Monday, 5 January 2015

Linguistic Premise Premise of Algebraic Linguistics 3-3 / September 24, 2007


Linguistic Premise

 Premise of Algebraic Linguistics 3-3

    TANAKA Akio

13 <tensor product>
A module MN
Tensor product     M A N
Given conditions
(1) M A is A module that is generated by { x ⊗ y | x My  N }
(2) ( x + x’ )  y = x  y + x’  y,   x  (y + y’ ) = x  x  y’     a  A   a x  y ) = ax  ay

14 <multiplicative set>
Ring     A
Subset of A     S
 S, 0  S
S is closed by multiplication.    
S is Multiplicative set.

15 <localization>
Ring     A
S is A multiplicative set,
S-1= { a/a  A S }
S-1A is ring.

16 <total quotient ring, canonical map>
Ring     A
Ring     = {  A | s is non-zero divisor }
S-1is total quotient ring.
A is subring of total quotient ring S-1A.
Canonical is next..
(1) Map iA : A  S-1A,   iA (= a/1
(2) Map iM  S-1M,   I (= x/1

Tokyo September 24, 2007
Sekinan Research Field of Language

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