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Page 1065 of Mathematical Reviews Vol. 48, Issue 4
[page]

1974
*
Mathematical Reviews
*

One consequence is that

*for*an open set U of*a**complete*variety X the property of being*semi*-*affine*depends only on*a*Zariski neighbourhood of the comple- ment. ... In § 3 it is shown that V is*semi*-*affine*if and only if I'( Y) is integral over ['(V)*for*all closed subvarieties Y. Also [(V) is shown to be finitely generated as*a*k-*algebra*when V is*semi*-*affine*. ...##
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Page 3150 of Mathematical Reviews Vol. , Issue 2002E
[page]

2002
*
Mathematical Reviews
*

Let g = g(

*A*) be an*affine*Lie*algebra*of type A3, (/ > 1) and W be its Weyl group. Let*A*be the root system of g and {ay,*a*),...,*a*/} be*a*fundamental system*for**A*. ...*For*J(V) this was shown in the previous work cited above. Then the authors use this result to give*a**criterion*of irreducibility*for**a*V-module. ...##
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Page 1332 of Mathematical Reviews Vol. , Issue 81D
[page]

1981
*
Mathematical Reviews
*

If f: XY is

*a**semi*-*algebraic*map between*semi*-*algebraic*subsets X, Y in R”, R” respectively, it is known that there exists*a*(dim Y — 1)-dimensional*semi*-*algebraic*subset Z of Y such that f is locally ... {*For*the entire collection see MR 80i:41004.} J. G. Timourian (Edmonton, Alta.) Hardt, Robert M. 81d:32012*Semi*-*algebraic*local-triviality in*semi*-*algebraic*mappings. Amer. J. ...##
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Invariant Ideals and Matsushima's Criterion
[article]

2005
*
arXiv
*
pre-print

This allows to obtain an elementary proof of Matsushima's

arXiv:math/0506430v1
fatcat:zzcqaxpeqja7db72qxmuchtj4e
*criterion*:*a*homogeneous space G/H is an*affine*variety if and only if H is reductive. ... Let G be*a*reductive*algebraic*group and H*a*closed subgroup of G. Explicit constructions of G-invariant ideals in the*algebra*K[G/H] are given. ... Hausen*for*useful discussions. In particular, Proposition 4.1 appears during such*a*discussion. Thanks are also due to D.A. Timashev*for*valuable remarks. ...##
###
On the complement of a nef and big divisor on an algebraic variety

1996
*
Mathematical proceedings of the Cambridge Philosophical Society (Print)
*

As is known,

doi:10.1017/s0305004100074983
fatcat:wfyriqokmnh47entfsm3u2gadq
*for**a**semi*-ample divisor D, R(X,D) is*a*finitely generated ^-*algebra*(see [21] or [9]), while this property is no longer true*for*arbitrary nef and big divisors (see [21] ). ... Then we show that, if D is*a*nef and big divisor, every divisor in \mD\ has*semi*-*affine*complement*for*every m ^ 1 if and only if Proj (R(X,D) ) is an*algebraic*variety over k. ... £) (/) = F(Xf) is*a*finitely generated ^-*algebra*; by Proposition 5 and Corollary 2, X f is*semi*-*affine**for*every feR(X,^C) + and then r^ is*a*proper morphism. ...##
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Page 6481 of Mathematical Reviews Vol. , Issue 96k
[page]

1996
*
Mathematical Reviews
*

From the main theorem (Satz 2.1)

*a*functional*completeness**criterion**for*Tg can also be derived. ... [The maximal classes of (),, €Q Pol, {*a*}*for*Q C E,, (*a**criterion**for*finite semiprimal*algebras*with only trivial subalgebras)| Rostock. Math. Kollog. No. 48 (1995), 27-46. ...##
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Page 6171 of Mathematical Reviews Vol. , Issue 2001I
[page]

2001
*
Mathematical Reviews
*

(English summary) [

*A**criterion**for*recognizing*algebraically*constructible functions] J. Reine Angew. Math. 526 (2000), 61-88. Let V be*a*real*algebraic*set. ... constant on each element of*a*finite*semi*-*algebraic*partition of V). ...##
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On Some Problems in Non-Commutative Probability

2021
*
figshare.com
*

are introduced

doi:10.6084/m9.figshare.14602638.v1
fatcat:qvd7xp3ypjfszpjdunssdoaeau
*for*it. ... We observe that if*A*is nonnegative, pseudo-pointwise admissible and*affine*thenΛ ∼ C π,y . ...##
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ON ALGEBRAIC VOLUME DENSITY PROPERTY

2016
*
Transformation groups
*

*A*smooth

*affine*

*algebraic*variety X equipped with an

*algebraic*volume form ω has the

*algebraic*volume density property (AVDP) if the Lie

*algebra*generated by

*complete*

*algebraic*vector fields of ω-divergence ... As an application of this method we establish AVDP

*for*any homogeneous space X = G/R that admits

*a*G-invariant

*algebraic*volume form where G is

*a*linear

*algebraic*group and R is

*a*closed reductive subgroup ... Acknowledgements: This research was started during

*a*visit of the first author to the University of Bern and continued during

*a*visit of the second author to the University of Miami, Coral Gables. ...

##
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On algebraic volume density property
[article]

2014
*
arXiv
*
pre-print

*A*smooth

*affine*

*algebraic*variety X equipped with an

*algebraic*volume form ω has the

*algebraic*volume density property (AVDP) if the Lie

*algebra*generated by

*completely*integrable

*algebraic*vector fields ... As an application of this method we establish AVDP

*for*any homogeneous space X=G/R that admits

*a*G-invariant

*algebraic*volume form where G is

*a*linear

*algebraic*group and R is

*a*closed reductive subgroup ... Acknowledgements: This research was started during

*a*visit of the first author to the University of Bern and continued during

*a*visit of the second author to the University of Miami, Coral Gables. ...

##
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A Ganzstellensatz for semi-algebraic sets and a boundedness criterion for rational functions
[article]

2014
*
arXiv
*
pre-print

We use this result to deduce

arXiv:1101.2116v5
fatcat:icg7hacrmjekjnei75lshzw2zq
*a**criterion**for**a*rational function to be bounded on an open*semi**algebraic*subset of some irreducible variety over*a*real closed field or over an ordered field which is dense ... Let 〈 K,ν〉 be*a*real closed valued field, and let S⊆ K^n be an open*semi*-*algebraic*set. ...*A*Ganzstellensatz*for*open*semi*-*algebraic*sets Let K be*a*real closed valued field, V some irreducible real*affine*variety over K, and L = K(V ). ...##
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Page 906 of Mathematical Reviews Vol. 46, Issue 4
[page]

1973
*
Mathematical Reviews
*

Under suitable separability assumptions,

*a*regularity*criterion*of the type “*A*, is regular if and only if D,(*A*), is free over*A*,” is deduced*for**semi*- analytic*A*. ... The localization of*a**semi*-analytic k-*algebra*at*a*prime ideal p is shown to have universal finite K-derivation*for**a*suitable field K>k. ...##
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Toroidal affine Nash groups
[article]

2016
*
arXiv
*
pre-print

*A*toroidal

*affine*Nash group is the

*affine*Nash group analogue of an anti-

*affine*

*algebraic*group. ... Nash group, and this H is toroidal. (2) If G is

*a*connected

*affine*Nash group, then there exist

*a*largest toroidal

*affine*Nash subgroup G and

*a*largest connected, normal, almost linear

*affine*Nash subgroup ... Next, we obtain

*a*useful

*criterion*

*for*toroidalness via

*algebraization*. Lemma 3.5. Let G be

*a*connected

*affine*Nash group and φ : G → G be an

*algebraization*. ...

##
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Open locally semi-algebraic maps

1988
*
Journal of Pure and Applied Algebra
*

This means that real spectra and

doi:10.1016/0022-4049(88)90017-5
fatcat:eowcwojdg5e5tl4y7wmldwmenq
*algebraic*properties of rings of sections of locally*semi*-*algebraic*spaces play*a*role. ... In*semi*-*algebraic*geometry examples of open morphisms occur naturally,*for*example coverings. ... We will prove*a*similar result on openness*for**semi*-*algebraic*mappings. Let f: M+N be*a*morphism of*affine**semi*-*algebraic*spaces. ...##
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Anti-affine algebraic groups
[article]

2008
*
arXiv
*
pre-print

We say that an

arXiv:0710.5211v3
fatcat:vwohxrkrkzfq5hccmc3mohphme
*algebraic*group G over*a*field is anti-*affine*if every regular function on G is constant. ... We obtain*a*classification of these groups, with applications to the structure of*algebraic*groups in positive characteristics, and to the construction of many counterexamples to Hilbert's fourteenth problem ... The preceding argument yields another*criterion**for**affineness*of*a*group scheme; namely, the existence of*a*faithful action on*a*variety having*a*fixed point. ...
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