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Limits of theory sequences over algebraically closed fields and applications

2004
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Discrete Applied Mathematics
*

It provides an approach to build a new

doi:10.1016/s0166-218x(03)00196-3
fatcat:yrjke6peozbttebplhfn6c4abe
*theory*by the*limit**of*some*sequence**of*formal*theories**and*also has potential*applications*to scientiÿc*and*engineering problems. ... A computation model involving the computation*of*the*limits**of**theory**sequences*is formally deÿned. It is called procedure scheme. ... Why to study*limits**of**theory**sequences**over**algebraically**closed*ÿelds As we have seen, during its execution, Analysis has to determine for a given w i whether w i ∈ L(G i−1 ) or w i ∈ L(G i−1 ). ...##
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Page 822 of Mathematical Reviews Vol. , Issue 99b
[page]

1991
*
Mathematical Reviews
*

Let K be an ordinary dif- ferential

*field*with char K = 0, differentiation D*and**algebraically**closed**field**of*constants Cx. ... The present paper fo- cuses on the sets*of*pseudo-*limits**of*such*sequences*. Every F- transcendental pseudo-convergent*sequence*defines a valuation on the rational function*field*F(X). ...##
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Page 101 of Mathematical Reviews Vol. , Issue 89A
[page]

1989
*
Mathematical Reviews
*

These groups are well behaved when the groups
H*(X,Z/I") are finite, which is the case when X is an

*algebraic*va- riety*over*a separably*closed**field*k*and*/ 4 chark. ... Correction to: “Notes on absolute Hodge cohomology” [*Applications**of**algebraic*K -*theory*to*algebraic*geometry*and*number*theory*, Part I, IT (Boulder, Colo., 1983), 35-68, Amer. Math. ...##
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Page 1736 of Mathematical Reviews Vol. , Issue 2000c
[page]

2000
*
Mathematical Reviews
*

Let K be an

*algebraically**closed**field**and*A = (Aj,---,A»)*and*X = (x,-++,Xn) systems*of*variables. ... Let K be an*algebraically**closed**field**of*arbitrary characteristic*and*let f, g € K[x]. The authors study conditions for f*and*g to satisfy f (g(x)) = g(f(x)). ...##
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Page 6197 of Mathematical Reviews Vol. , Issue 98J
[page]

1998
*
Mathematical Reviews
*

As an

*application*, the authors re-prove Saltman’s index reduction theorem for the index*of*a simple*algebra**over*the func- tion*field**of*a principal homogeneous space for a torus [D. J. ... Saltman, K-*Theory*7 (1993), no. 4, 309-332; MR 94k:16049]. Fi- nally, they give generators*and*relations for Ko*of*a torus*over*a*field*. ...##
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Page 686 of Mathematical Reviews Vol. 48, Issue 3
[page]

1974
*
Mathematical Reviews
*

Zham (Bratislava)

*ALGEBRAIC*NUMBER*THEORY*,*FIELD**THEORY**AND*POLYNOMIALS See also 3895, 3945, 3965, 4696. Smyth, C. J. 3912*Closed*sets*of**algebraic*numbers in complete*fields*. ...*ALGEBRAIC*NUMBER*THEORY*,*FIELD**THEORY**AND*POLYNOMIALS 686 Choi, S. L. G. 3910 On*sequences*not containing a large sum-free subse- quence. Proc. Amer. Math. Soc. 41 (1973), 415-418. ...##
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Page 79 of Mathematical Reviews Vol. , Issue 84a
[page]

1984
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Mathematical Reviews
*

Grayson, Finite generation

*of*K-groups*of*a curve*over*a finite*field*(after Daniel Quillen) (pp. 69-90); Howard Hiller, Affine Lie*algebras**and**algebraic*K-*theory*(pp. 91-107); Johannes Huebschmann, Stem ... Wagoner, A picture description*of*the boundary map in*algebraic*K-*theory*(pp. 362-389); C. A. Weibel, Mayer-Vietoris*sequences**and*mod p K-*theory*(pp. 390-407). ...##
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Page 635 of Mathematical Reviews Vol. , Issue 89B
[page]

1989
*
Mathematical Reviews
*

More im- portant, groups

*of*finite Morley rank are very similar to*algebraic*groups,*and*rings, to finite-dimensional*algebras**over**algebraically**closed**fields*, etc. ... In par- ticular, tree-*limits*were applied to certain problems concerning existentially*closed*groups, skew*fields**and*universal locally finite groups. ...##
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A new matrix model for noncommutative field theory

2004
*
Physics Letters B
*

The construction is based on the Elliott-Evans inductive

doi:10.1016/j.physletb.2003.10.059
fatcat:fjuod3ewejdvxjxik7nhf65rhy
*limit*decomposition*of*the noncommutative torus*algebra*. ... We describe a new regularization*of*quantum*field**theory*on the noncommutative torus by means*of*one-dimensional matrix models. ... Mechanics Three*applications*• Perturbative Dynamics*of*φ 4*theory*Graphs have ribbon structure. ...##
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Modular representations and the cohomology of finite groups

1987
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Topology and its Applications
*

in

doi:10.1016/0166-8641(87)90014-9
fatcat:5pk45mx5pnh5zkjsoae35pbe7y
*algebraic*K-*theory*. ... We discuss both this result*and*the analogue for finite*fields*, using facts about H*(G, iZ/r) to recover information on RF,(G). ... In order to prove that the inverse*limits**of*the homotopy sets are isomorphic we consider the inverse*limit*spectral*sequences*for topological*and**algebraic*K-*theory*. ...##
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Page 2620 of Mathematical Reviews Vol. , Issue 84g
[page]

1984
*
Mathematical Reviews
*

Burgin, Kurosh
varieties

*of*Q-*algebras*that are linear*over*a*field*(pp. 17-27). ... The following four classes are introduced: ® is the smallest class*of*short exact*sequences**closed*under direct*limits**and*containing 2; Si’ is the class*of*all short exact*sequences*which are direct*limits*...##
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Stable étale realization and étale cobordism

2007
*
Advances in Mathematics
*

Finally, we construct maps from

doi:10.1016/j.aim.2007.03.005
fatcat:rh7ruhmnxfd2zgdlihtdkdozxe
*algebraic*to étale cobordism*and*discuss*algebraic*cobordism with finite coefficients*over*an*algebraically**closed**field*after inverting a Bott element. ... We show that there is a stable homotopy*theory**of*profinite spaces*and*use it for two main*applications*. ... Acknowledgments I would like to use this opportunity to thank first*of*all Christopher Deninger for the suggestion to work on this topic. ...##
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Definable types in algebraically closed valued fields
[article]

2014
*
arXiv
*
pre-print

Marker

arXiv:1410.3589v1
fatcat:4hwisvh3vbdupbid3qfmdkpwy4
*and*Steinhorn shown that given two models M≺ N*of*an o-minimal*theory*, if all 1-types*over*M realized in N are definable, then all types*over*M realized in N are definable. ... In this article we characterize pairs*of**algebraically**closed*valued*fields*satisfying the same property. ... Let k be an*algebraically**closed**field**and*K = k(X, Y ) a with 0 = v(k) < v(X) << v(Y ). ...##
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New Definitions of Sigma Field

2020
*
Journal of Southwest Jiaotong University
*

The main aim

doi:10.35741/issn.0258-2724.55.1.15
fatcat:cfw5xremkrde7pp7hd3xw76sou
*of*this paper is to define the sigma*field*. Different types*of*sigma*fields*, along with the basic mathematics*and*examples, are also elaborated upon. ... The sigma*field*is a branch*of*mathematics that refers to the gathering*of*subsets includes sample space. It is useful in establishing a formal mathematical probability definition. ... ACKNOWLEDGMENTS The Author is thankful to Directorate*of*Education, Salah Eddin, Khaled Ibn Al Walid School for their kind support. ...##
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Page 1653 of Mathematical Reviews Vol. 49, Issue 5
[page]

1975
*
Mathematical Reviews
*

Other

*applications**of*the M.V.*sequence*are given by the reviewer*and*M. Ojanguren [J. Pure Appl.*Algebra*5 (1974), 345-360]. ... K-*theory**sequence*for the category Pic*of*Milnor*and*Bass is extended by the author to a long exact*sequence**of*Cech cohomology with value in the units. ...
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