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8/10/2019 Valuation on Some Algebric Structures by M. H.
Hosseini and M. H. Rezaeigol
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() ()
&
()
. . . .
A M M, B, IA.
( : J 4, 2014)
(
), ( ) , ,
1
I , ()
, .
1.1.( 1) A
, , ,
1) () = () + ();2) ( + ) (), ();3) () = = 0.
, (1)=0 = ()
.
1.3.I = , .
1.2.L . M , (/) = ,
0 ,
.
A = (), /, 0,
.
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8/10/2019 Valuation on Some Algebric Structures by M. H.
Hosseini and M. H. Rezaeigol
2/4
333 , & (), ()
, (/) = () ()
.
2.
L () . F :
G = ( ,)= ( ,) (), , ,
= (+ ,)
2.1.( 3). A ( )
()
: ,
:
(1) () < , = ;
(2) , , 1 , =, =, 1 , = ;
(3) , , , , ;
(4) , = + ;(5) = 0, .
. . : .
, ()= () .
. . L .
= (), 1 :
= ,,D D
, () = .. ( 5).
2.4. 2.2 2.3
= ().
3.
L () . A ( 7, C. I,
II).
3.1.A
()
: () ,
:(1) () () < , () = ;
=
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8/10/2019 Valuation on Some Algebric Structures by M. H.
Hosseini and M. H. Rezaeigol
3/4
, & (), () 334
(2), (),1 , =, =, 1
, () = ();(3), (), , () (), ();(4) ,() = () + ();(5) = 0, .
3.2. 2.2, 2.3
2.4, .
4.
I ,
.
4.1.().L .
() () ()
,
, ,
, , , ( ). .
, , , ( =1, 2, , ).
= ( 2) , = . :
4.2. M
() () ()
5.
I ,
, , .M =, , , .
5.1.L
. A
, :F , , + (), ();I() (), , ,() () ;= = .I,, , (), () () ;
() F (
() ), (()) = (). I , () .
5.2() .
. .F ,
, :
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8/10/2019 Valuation on Some Algebric Structures by M. H.
Hosseini and M. H. Rezaeigol
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335 , & (), ()
(1) F , () = 1 = 0;
(2) F , , ( + ) (), ();(3) F , () =().
,
M . I ,
0, (, 0).
5.4.. L
F (.., F) B
F . F ,
=+ + +
, , , , , , 0.
=
B=, 0=
0.
1.
. M. C,
, ., . 54, . 1 45 (1989).
2. . G, M, , 35:8, 2341
2356.
3.
M. H. H, H ,
, . 140, . 2, (2007).4. . . L, A , , (1991).
5.
M. MH,
, ,
1(4): 347351 (1995).
6. . F. G. , , . 51,297 304 (1945).
7. . . , M A , F,
M (1960).
