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Page 1401 of Mathematical Reviews Vol. , Issue 85d
[page]

1985
*
Mathematical Reviews
*

There are three main results

*in*this paper, all concerning the enveloping algebra A of a solvable Lie algebra g,*finite*-dimensional over a field k of*characteristic*0. ... -3*ring*Q, which is a two-sided maximal quotient*ring*, with minimal faithful modules*Qe*and fQ such that F is a subring of Q containing*Qe*and fQ. ...##
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Algebraic Dependence of Arithmetic Functions

1962
*
Indagationes Mathematicae (Proceedings)
*

with the multiplication

doi:10.1016/s1385-7258(62)50015-2
fatcat:ipm4ifgnkvggbon3wahwuxcmae
*in*the*ring*R. ... Such a*ring*(e.g. an integral domain of*characteristic*zero) shall be called torsionfree.Theorem 2. Let R be torsion-free. Let /1, /2, ... , fr be algebraically dependent over R'. ...##
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Variations on a theme of Minkowski and Serre

1996
*
Journal of Pure and Applied Algebra
*

If CL is a root of unity

doi:10.1016/0022-4049(95)00113-1
fatcat:jaagmtwdcbg27onbviwjgsusa4
*in*an integral domain 0 of*characteristic*zero, (a -l)k E no, and no prime divisor of n is a unit*in*0, then a = 1 if n is a positive integer outside a*finite*set determined by ... Notation All*rings**in*this paper are*rings*with identity. However, we do not assume 0 # 1; that is, we do not exclude the zero*ring*. ... Then cxRckP) = 1;*in*particular, CC= 1 ifn$N(k).*Rings**in**characteristic*zero Remark 4.1. ...##
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Page 1261 of Mathematical Reviews Vol. 46, Issue 5
[page]

1973
*
Mathematical Reviews
*

If P is a generator

*in*the category of right A-modules such that the*ring*B is semiprime, then P is of*finite*type and projective. J. Inh (Raleigh, N.C.) ... One also finds there Brauer’s useful result that, if R is a field, the class of M*in*G,*(A) is determined by the*characteristic*polynomials on M of the elements of A. ...##
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Page 618 of Mathematical Reviews Vol. 46, Issue 3
[page]

1973
*
Mathematical Reviews
*

Authors’ summary: “Let F be a

*finite*extension of the p-adic rational field Q,, R, a*ring*of integers*in*F and A,(R,G) an algebra of R,-representations of a*finite*group G over the rational field Q. ... No. 40 (1971), 81- 116] by considering families 6={G(q)}, of type (W, R), where (W, R) is a*finite*Coxeter system, q runs through a fixed infinite set €P (= “*characteristic*powers”) of prime powers and ...##
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Trace and defect of a block idempotent

1990
*
Journal of Algebra
*

DEDICATED TO WALTER FEIT ON THE OCCASION OF HIS 60TH BIRTHDAY

doi:10.1016/0021-8693(90)90190-y
fatcat:r37ist5cmbfgpj723suwv2fggq
*In*the study of group*rings*SG of groups G over fields S of*characteristic*zero the trace tr(a) of an idempotent a = CgeG s,g, SUE S, is defined ...*In*fact by Theorem 2.1(b) tr(i) = ~"-~x/y, where x and y are integers which are not divisible by p. Since for every idempotent*QE*SG the trace tr(a) = IGI -' dim. ... visit*in*1988. ...##
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A note on reduced Jordan algebras

1968
*
Proceedings of the American Mathematical Society
*

Since p\ei= UPie}e2 = UV{ei)ese2=Ue1Ue2Ue1e2=pip2piei we have

doi:10.1090/s0002-9939-1968-0227241-2
fatcat:75nbg2nvsfbgrh3uv6ublzcuze
*p2*(pi-*p2*)=0; similarly*P2*(*P2*-Pi)=0, so either pi-*p2*= 0 or Pi=*p2*= 0, and*in*either case Pi=*p2*=p. ...*In*this section we make no assumptions about the simplicity or*finite*-dimensionality of A. Recall that an idempotent e is reduced if Ai(e) = UeA=$e. ...##
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A Note on Reduced Jordan Algebras

1968
*
Proceedings of the American Mathematical Society
*

Since p\ei= UPie}e2 = UV{ei)ese2=Ue1Ue2Ue1e2=pip2piei we have

doi:10.2307/2035351
fatcat:yii5aulni5gjlokvc3fzjbn7ce
*p2*(pi-*p2*)=0; similarly*P2*(*P2*-Pi)=0, so either pi-*p2*= 0 or Pi=*p2*= 0, and*in*either case Pi=*p2*=p. ...*In*this section we make no assumptions about the simplicity or*finite*-dimensionality of A. Recall that an idempotent e is reduced if Ai(e) = UeA=$e. ...##
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A Design and an Implementation of an Inverse Kinematics Computation in Robotics Using Real Quantifier Elimination based on Comprehensive Gröbner Systems
[article]

2021
*
arXiv
*
pre-print

Furthermore, pre-computation of CGS and substituting parameters

arXiv:2111.00384v1
fatcat:nwumg2ilozagjjtcxitn275ica
*in*the CGS with the given values avoids the repetitive computation of Gr\"obner basis. ... Then, the quotient*ring*K[ X]/I is regarded as*finite*dimensional vector space over K [3] ; let {v 1 , . . . , v d } be its basis. ...*In*Step*P2*, we choose F ⊂ F satisfying that S lj contains real points and the system of polynomial equations*in*eq. ( 12 ) has*finite*number of roots for c ∈ S lj . ...##
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Torsion-Free Abelian Group Rings III

1977
*
Bulletin of the Faculty of Science Ibaraki University Series A Mathematics
*

Assume
G
be

doi:10.5036/bfsiu1968.9.1
fatcat:643f2rjrujcudjqnu7mgfquqtm
*finitely*generated and _??_ a prime ideal of qKG[X]=*qe**in*KG[X]. Then, _??_•¿ kG[X]=P. PROOF. By Prop. 3,*qe*: _??_ce=(q: _??_c)e. Hence, By Prop. 1, Hence, _?? ... Let F'G'•¸*qe*for F', G'•¸S and G'•¸*qe*. We may suppose F' , G' E k[t]G[X]. By [29] (6.15), qR[t] is primary*in*R[t]. ...##
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The Brauer-Wall group of a commutative ring

1971
*
Transactions of the American Mathematical Society
*

The Brauer-Wall group is therefore a fundamental tool towards a general theory of quadratic forms (over an arbitrary commutative

doi:10.1090/s0002-9947-1971-0276218-4
fatcat:rcp2v6nmrzawxai5dxs4gqcsnu
*ring*). This theme is developed*in*[3, Chapter V]. ... Brauer group of a commutative*ring*, separable algebra, Azumaya algebra, graded algebra, Galois extension of commutative*rings*, quadratic extension of commutative*rings*. 0) This paper contains part of the ... When A has*characteristic*2, A{a} is a*QE*of A: for any a g A:, and*in*fact all QE's are of this form ; the crossed product described above is then m When 2 g Uik), \k(a)\ is a*QE*for any a e ¿/(A), and ...##
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The Brauer-Wall Group of a Commutative Ring

1971
*
Transactions of the American Mathematical Society
*

The Brauer-Wall group is therefore a fundamental tool towards a general theory of quadratic forms (over an arbitrary commutative

doi:10.2307/1995622
fatcat:gn3stq2fxjbq3ovn2doe6km3iu
*ring*). This theme is developed*in*[3, Chapter V]. ... Brauer group of a commutative*ring*, separable algebra, Azumaya algebra, graded algebra, Galois extension of commutative*rings*, quadratic extension of commutative*rings*. 0) This paper contains part of the ... When A has*characteristic*2, A{a} is a*QE*of A: for any a g A:, and*in*fact all QE's are of this form ; the crossed product described above is then m When 2 g Uik), \k(a)\ is a*QE*for any a e ¿/(A), and ...##
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F-jumping and F-Jacobian ideals for hypersurfaces
[article]

2013
*
arXiv
*
pre-print

We introduce two families of ideals, F-jumping ideals and F-Jacobian ideals,

arXiv:1302.3327v2
fatcat:it37txycn5chxhxxvvdzyyayqy
*in*order to study the singularities of hypersurfaces*in*positive*characteristic*. ...*In*addition, we use F-Jacobian ideals to study intrinsic properties of the singularities of hypersurfaces.*In*particular, we give conditions for F-regularity. ... Let R be a reduced*ring*essentially of*finite*type over an excellent local*ring*of prime*characteristic*. ...##
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On rings whose Morita class is represented by matrix rings

1998
*
Journal of Pure and Applied Algebra
*

*In*the description of

*rings*of this type, Picard progenerators and (

*in*the commutative case) the Picard group play a significant role. ...

*In*a number of special cases these two conditions will also become sufficient. ... We are grateful to Ken Goodearl for drawing our attention to the class of ultramatricial von Neumann regular

*rings*as a useful source of examples of MM

*rings*and to Roger Wiegand for helpfkl conversations ...

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Quaternion constituents of group algebras

1971
*
Proceedings of the American Mathematical Society
*

*In*this paper it is shown that each quaternion division algebra central over the rationals appears as a division

*ring*constituent of some rational group algebra. ... Let x be an irreducible character of a

*finite*group and let A be a field of

*characteristic*0. ... To compute mQp(d) we use a theorem of Kronstein [4] Thus we have mQq(x) = 2 ii q = p or oo and mQq(x) = 1 if

*qE*{2, p, oo }.

*In*particular wq(x) = 2 and the constituent Z? ...

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