SCIENTIFIC ABSTRACT FADDEYEV, D.K. - FADDEYEV, L.D.

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• Document Creation Date: January 3, 2017
• Document Release Date: July 28, 2000
• Sequence Number: 18
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

Cb uravm.-rdl ZLI'A-By4=6; 6=1,:',4.q8j L.j Ucly-al. -d,
SO: Lati-cmatia; in the USSIR, 1 17-1,247
cdit-,~d by Jurosh, A.G.J.
larlmshevich, t.L.)
It , .~:.
191#8

0 plotnoAyal-h tselyldi tache", cl',irto
razliclhn. i:a .-,ru,-~:-ard Galua. I,J.* ai~r. 133.
SO: Lat;~oii~ttics in tho OSSR) 1:,;'7-1-,'47
editod b-~ Jur.),sh, A.Gf)
1,,--.r';:u!~hcvlcL, A.L.J
...Or,co-.-.-Lun!nj-,rad,

FADD-EY-EV, D. K.
Construction of Fields of Alvebraica-1 N,,,ml)p-.rs J.,qjose G-Ijois Group is a Group of
Quaternion Units, Doklady AN SSSR, 47, No. 6, 1945-
Leningrad Branch, Mathematics Inst. im V. A. Steklov, AS USSR
Presented: 1944
On a Problem of Analytical Geometry, Doklady All SSSR, 47, No. 8, 1945.

UM/Jftth4MtlcS - O"MtIODSI 'Tk*Cr7 Oct 194T
Wthewtice - Algebra, Complex
OFlactior Systems in Abelev's Groups With Operatoropw
D. K. Faddeyev, Leningrad DeRt, Yath Iust ineml V.
A. Steklov$ Acad Sci USM, :ir pp
ml)ok Akad Nauk SM, Nova Ser" Vol LVIII, No 3
Diamesee varlons variations of the basic problest.
2xPlaIns the k-faotor-system if A Is the addItlysly
recorded Abelev group and 7 the group whose elemazte
are the operators of A. Also discusses the varla-
t1on where b is sma additively recorded Abele'r I
group and r is some group. Mrplains the Tairiation
vhero b Is the Abelev group vIth 7 the operative
49T43
U8W/M%th4Md,ticO - OPOrstlOual ThOCU7 Oct 2947
(Cmtd)
gr and A the supplementaz7 subgroup. Submitted
by Academician I. X. Vinograday, 28 Apr 194T.
49T43

series Iffor 3.947
"Structure of the pnq Series Group," D. X. Faddeyev)
Imin,grad Branch, Mathematical Institute imeni V. A.
Steklov, Academy of Sciences of the USM, 2 pp
03)ok Ak NaukH Vol LVIII, No 4
Discusaes folloving theorem: If the pnq series group
him neither a- norml denominator of the pn series,
ncw a normal denominator of the q sericpj then pp'q
fulfill the requirements: q-=Il(p),p er,,.) 4 n- l..
ftere r is the smallest of the positive numbers so
that P'$~-- l(q). It is evident that cnljr the f Inal
mluas for the sinple im ' are pq, vil.1 fulf ill the
ocnditions for the given n, so that even the group Of
~L 38T64
n I P /*thwatice - Series, (Ccntd) Nov 1947
the pAq secries, vhioh does not have strcog ngrmal
denaninators, VM confom only to the fAnal M27ober
mhere n is'fixed. Submitted by Academician 1. M.
VInQgradov 28 A;r 1947.
38r64

U8SR/)ftUew&t1cw3 .6 PktrIces NOV 194T
Nlathemtloe - Xquatims
"MAraoteristle Equations of Ratioun' Symmetrical
Jktrloes," D. K. Faddeyev, Leningrad Branch, Mathe-
motics Institute imeni V. A. Steklov, Academy of Sol-
owes of the 2 pp
"Dok Ak Nauk" Vol LVIII, No 5
Several theories have been submitted with regard to
the requirements of a rational coefficient to be obar%
actarlstic for equations of rational symwtrical
matrices. Author discusses yet another theory, which
In a fairly broad conception, yet Is lirafted enough
so that it can be utilized for equations of the
38T68
MR/*thmatics - 3ktriww (Cmt&) lbw 194T
Oeventh order. Statewhis theor and gives ItA
proof M.N.D.). Submitted by Acadmiclan 1. X.
Vlnogradov, 28 Apr 194T.
38M
k4

USSR/Vkthemtics - Acadaw of Nov/Doc 50
Sciences
"Boris Nikolayevich Delone," D. K. Faddeyev
"uoekh matemst Nauk" vol v, No 6(4o), pp 159-163
Biogmphy of great Russian mathematician vho
celeb-ated his 6oth birthday 15 Mar 50. Prof
Delone is Corr Mm Aced Sci USSR. He studied at
Kiev U 1908 - 1913. Much of his work has been in
the theory of Galois groups. Delone teaches
mthematical an&2,vais, analytical geometry,
USSR/Kathematics - Academy of Nov/Dec 50
Sciences (Contd)
non-Inclidean geometry, Galois theory, mathe-
matical crystallography, theory of computing
amLckdaes, etc., at the Moscow and Leningrad
Universities. He is an Alpinist.
17M69

1. FADDEMs D. K.
2. ussR (6oo)
h. Science
1 7. Algebrae Textbook for teachers of seventh grade. Pt, I. Leningradj Uchpedgiz,, 1951
9. Monthly List of Russian Accessions, Library of Congress, January, .1953. Unclassified.

*Faddeey, D. K. Simple algebras over a field of algebrith: Let now A bit! a global central simple algebra, For every '-14
divisor p of k we have a local algebra A. over tl-.e local field 'd
functions of one varialSTe-,7j-tj-(Jv Mat. Inst. Steldov., k which is a field of power series over the inertial field k,
v. 38, pp. 321-344. lzdat. Abd.'Nauk SSSR, Moscow,
1951. (Russian) 20 rubles. of p, The algebra A, has as its invariant the cyclic pair
'rhe constint field ke for thealgelyraic func-finrip is always defined above, and these cyclic pairs satisfy a product
formula
r field. The pr7Te-fYi i.~ t7o ~1-a-
art algebraic nunibe '"ify sirnple
algcbras over k -ko(x. y), where x is an indeterminate and y
is algebraic over ko(x), Any simple algebra over kq can he The definition of the norm and product of cyclic Pairs Is
lifted tip to one overk; the rcsult iscalled a numerical alge, tco lengthy to reproduce here; it uses Galois theory,
bra. The principle of classification is the follow;ng: two character frroups and the transfer (Verlagerun ) of a RMP
9
algebras over h are similar in the wide sense if one is simiLir
in the ordinary sense to the product of the other by a into a subgroup. Finally, k is specialized to the field ka(x)
numerical alvebra. of ratinnal functions, and it i9 shown that the local invari-
After soine exfx)-,itnry material, the atithor take-3 tilt the ants of A characterize A tip to Fimilarity in the wide sense.
local theory. Let A be a central division algebra over the Momover thtre exists an algebra for any aet of invariants
ficN of formal power'series in r. IFhe center Z of the sat isfying the product formula. I.. Kaplatf sky.
inertial itigebra turrill out to blo cyclic over k*. U If is an
clernent of mininial positivc value in A. then the inner
autornorplihm by Ff induces an autoinorphism r of Z. The.
"cyclic pair" (Z, r) is shown to be a complete r
,ct of invari-
antq for A under similarity in the wide sense. The theory
extends to the simple cask-.
Sourcat Vathwnaticel Raviewa, Vol
J~j NO.10

t-- Vi
Faddeer, D. X 1. S. Sbornlk zadal po
- , Sominskil,
matimatioal Reviews vystel algebre. -LCollection of problems ov. hlgher
Vol. 14 No. 11 idgebra.1 3d ed. Gostidarst~. lzdat. Telm.-Tcor. Lit..
Deoemberi, -Tro-sc-o-w-Teningrad, 1952. 308 pp. 7.20 rubles.
Part 1, Problems: 1) Complex numbers; (1) Computation
Alsebra.
lei of determina-its; M) Systems of linear equations-, IV)
Matrices; V) Polynomials and rational functions of one
variable; VI) Symmetric functions; VII) Linear algebra.
Part 2, Hitits. Part 3, Answers and solutions.
------ Table vf Conkids.

C t_

in
"Faddeev, D. K. On this theoty o~~qtq~ for yr1f; there is an explirit ism-norphism between
C-.(G, 1)
`~Izvc
stiya Akad. Nauk SSSR. Ser, blat. 16. 17-22 (1952). tt!on-iiitiiiiietieciuscocti~Lins)aitdC. (G.11.A),commuting
(Russian) With coboundaty. It renming to prove t 01 t
Fhe author studies a relation between the cohontotogy
11,+,(G, 11. A) -If.-t,(H, 11, A)
nd those of a ejubgroup 11. Let G
groups of a group G, a
opeiate on the right of tile additive group A, and let i be the isomorphism induced by restriction of the functions tall,
the additive group of functions from Cie sct jpj of right This i-s shown by induction: an important role is played by
Cosets. of 11;n 0 to A, with G operating by P(p) -U(Ar-1)J,. the theorem that for ti-_2 -nll 1r.(G,11,b)-O, where b
Theorem: Theisoniorphism is de. 'is tile group of all functions front It to A, with it olwrat;ng
rived from the chain map q (the y, run through it; p,- If): by fv.(y) - [f(yyj-l)3F'. Reviewer's note: An interpretation
?F(yi, y.) - F(yi, y.)(po). The proof utilires a num- of the author's result can be obtained by rioting that tile
ber of other groups; C.(G,, 11, A) is the group of -11-homa- Eilenberg-NfacLane space of 11 is a covering space of
geneous cochains (on G with values in A): that of G.
H. Sit"(1son (Ann Arbor. Alicll,).
Axly. X.Y) -P(xtl ... I Xfo)

Sourcat Mathematical Raviews, Vol 11 NO,

FAM)FYI-I'V, D. K - , Prof .
Chebyshev, P. L.
"New collection of L. L. Chebysbev's whtings." Vest. All SS'R, 22, No. 5. 1952.
Monthly Ligit Qf Ibiggsian Acceasions- Library of Conpress, October 1952. Unclassified.

0
On it theorem of the theory of homo?oe#*
in gr2yo Voklady Aka4 Nauk SVSPL (N.S.) 92, 704-
705 (1953). (Runian) "Wofagroupe.1falsa
It b is a subgroup of finite ind
0-module in whIch divition'by ft Is always poaMe and
unique, then the cohomology module R*(W, a) Is IsomorphIc
with a direct summand of 91, B. X K*Aifs.

Um'I "; SOMINSIIT, I.S.; BARKOVSIIT, I.V., redaktor; MAKRUSHIN. V.A..
- UMM'ofieekty redaktor
[Algebra. Pt.2.'Kwmal for secondarv school teachers) Algebra*
Chast' IL Posobie d11& uchitelel erednet shkolr. Lehingrail, Goo.
uchabno-podagog. izd-vo Ministerstva, proeveshchanita RUSR, 1954.
286 p. (Algabra-Study and teaching) (mm 8:3)

to,, yKon.~km1w 3 ~ t ii
YAMMM, D.N.; SDMINGKIT, I.S.
[Collection of problem in hishor algebra]
po Vushel algebre. Ind. 5-o, stor*otlpnoo.
tekhdko-teor6t. lit-ry, 1954. 308 P.
(Algebra--Problem. exercises. ate.)
Sbornik sadach
Kooky&, Go@. isd-vo
(K6U 7 0- 8)

7
~addisv, D. K, On a linothesla of Elmo. Daklady
Akad. Nauk SSSR (N.S.) 94,1013-1016 (1954). (Rus-
Slan
Ut k1k, une extension galoinientie finie, dont r soit 1e
pe de Galois. 0 ktant tin groupe donn6 Wavance, Oont
rou
g
r eat une image homomorphe, et v 6tant ui) licimornorphisme
crit de 0 sur r, 11 se post la question dti [a possi~HU6
I immersion de k1ka done une alg6re galoisienne (au sens
do Hasse) de groupe 0,'cette immerbion Atant telle que
Llk
11jipplication, canonique de 0 sur le groupe de Galois de k1ko
Wricide avec P. Lauteur avait donn6, dons un travail
antirieur [Mat. Sbornik NS. 15(57), 243-784 (1944); ces
iRev. 6, M], ensemble avec B. Delaurtay, la condition
Ocestialre'que voicl de cette immenibilit6, appel6e "condi.
0'fi do
64rence": j'ftant lo ngya4 de v, considdrons 0
'iomwe iiii groups, d'op6rateura de Panneau de groupe I
~'de C our It, en poeant, pour tout v e G, a-a-*0(,j si a 8 k et
on posant a - r - o-lrq, quand r t 1. Alors, la condition de
-ence consisto en 1existence do I-coc
coh6 haine de 0 A!
1, Coefficients done 1e demilroupe muttiplicatif de S-k, qui
soft un cocycle et dont la restriction A g Poit r-1.

law,
&~i'un ci~; Ous' &'infral. it kalenitnt onn6 une
candit;on n6cemalte d'une telle immersibilM, qui r,-- houve
We ~qulvalentp., dans le W consid6t, & ]a condition
prk6dente. 11 a &nis Phypoth&,~ que cette condition nhes.
milre d'inimernibilith est aussi suffisante. L'auteur montm,
tAr un cantre-exemple, qui ne fait Intervenir que lea rom-
j p-*Aa deg extensions quadratiques, qu'il Wen est rien.
M. Kraitter
(Paris),

YAMUV, D.X.
An aritbmetto formal&. Usp.matnauke 10 no.1:169-171 155
(Tiolds. Algebraic) (KL4A 8:6)

groups of.
loi ad. Nauk SSSIC Ser. Mat, 19, 193--
. v,, A k
be a~ ussian)
group, H a subgroup, A a G-module. For
any Integer rsZO the elements I a C"(G, A) v.,hich, in their
hoinogencous form, depend only on the right cost-As of
G mod It In which the arguments lif., form
a subgroup,
C4,"(G. H. A) of CO(G. A); by definition Z,"(G, H,.4)=
Z"(G, A) r%C,*(G, H,A), B,O(G, H, A) G, H, .4) and,
Ho"(C-P. 11,A) "IG- H A)ID /I is normal!
inlgthenHo [These definitions
and remark, but not the notation, arc much as in Adarn-
son, Proc. Glasgow Math. Assoc. 2, 66-76 (1954) (MR 16,
442) where with the added hypothesis that H is of finite
Index in G the definitions are extended to permit negative
n.) Now let G have order hk, H have order h. h and A
being relatively prime, because hkll"(G, .4)=O, there is
a uniquedirect decomposition
where kff,"(G,A)--,O and h[1,'1(G,A)-O. T'he
main eorem 1) asserts that 1: H,"(G, 11, A)
result
1."'" '. Al al' H,-(G A)wll -(. If, A), where A and & are
lift and restriction ho~iomorpLi'sms, and H.2(11. A) s a (CL)
certain direct summand of H*(H. A). As a corollary one

------ -------
-- --------

T

his ffbemm 2). for any finite group G, Hl,,(G, 4) ow'! q
EM I(S 'A) (direct sum), where P runs over the set of
primes Jividiq the order of G, and S
is a p-Sylow
,
Ch
subgroup of G. The special case of Th -orem I in wilt 9
at in G was given by Ho-chschild and Serre
is norm
(Trans. Amer Hath. Sm. 74, 110-134 (1953): MR 14,
619. E, R. Kokhioi (New York, N.K.).

4'$

dd"V. D. K. On the concept of norm of a SIMRIe
Ia Dokl. Akad. Nauk SSSR (N.S.) 105
(1955), 662-663.
Lct
~o be a field, kj a finite separable extension of ko,
e
11 a Untral simple algebra over ki, M. Kneser [Arch.
math. 4 (1953), 97-99; MR 14, 1058~ defined the norm
N&,jk,(a),* it is a central simple algebra over ko. After
observing (Th. 1) that Nk,;k,(tl)=-.- A'k,ik.(,V,,,/k,(a)), the
author shows (Th. 2) that if, for any extension K of "co.
one %vrites K - k, ='~' S, (oircct surn of fields) and ag=
Ejj (direct sum, al curitral siniple over KI), then
Ne%t, iSSIL111ing that ko is a
p-adic field and p, is a of k, over p, he proves
(Th. 3) that passing to the norin leaves invariant the
invariant of a at pl, ix. (11,;PJ) ~= This permits
him to prove (TI, 4) that if kc, is an algebraic number
field of finite degrec %vith place ~, and p I, - - -. p,, are the
places of hI into which p factors, then (Nk,1k,(a)1P)=
E. R, Kolchin (Ne%v York, N.Y.).

TRANSLATION FROM:
AUTHOR:
TITLE:
PERIODICAL:
ABSTRACT:
Card 1/1
44-1-140
Referativnyy zhurnal, Matematika, 1957, Nr
P 17, (USSR)
Borevich, Z.I., Faddeyev, D.K.
On the Theory of Holmology In Oroups
(K teorii gomologiy v gruppakh)
Tr- 3-90 Vaes. matem. s"yezda, 2, Noscow,
AN SSSR, 1956, p ill
Bibliographic entry
1,

_M
'SUBJECT USSR/UATHEMATICS/Ther)ry of probability CARD 705
AUTHOR FADDEEV D.K.
TITLE On the notion of the entropy of a finite.se-heme ~f probability.
PERIODICAL Uspechi mat.11auk 11, 1, 227-231 (1956)
reviewed 4/1957
The entropy H(PVP21 ... 'Pn) of the probability distribution (P19P29 ... ~Pn)
n
(where n is an arbitrary integer ~~2, Pk?-O an d E, Pk - 7) is ~karactet~zad
k-1
by the following three axioms: 1) H(p,l-p) is a continuous function cf p
(0