Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finitely Supported *-Simple Complete Ideals in a Regular Local Ring   Let I be a finitely supported complete m-primary ideal of a regular local
ring (R, m). A theorem of Lipman implies that I has a unique factorization as a
*-product of special *-simple complete ideals with possibly negative exponents
for some of the factors. The existence of negative exponents occurs if the
dimension of R is at least 3 because of the existence of finitely supported
*-simple ideals that are not special. We consider properties of special
*-simple complete ideals such as their Rees valuations and point basis. Let (R,
m) be a d-dimensional equicharacterstic regular local ring with m = (x_1, ...,
x_d)R. We define monomial quadratic transforms of R and consider transforms and
inverse transforms of monomial ideals. For a large class of monomial ideals I
that includes complete inverse transforms, we prove that the minimal number of
generators of I is completely determined by the order of I. We give necessary
and sufficient conditions for the complete inverse transform of a *-product of
monomial ideals to be the *-product of the complete inverse transforms of the
factors. This yields examples of finitely supported *-simple monomial ideals
that are not special. We prove that a finitely supported *-simple monomial
ideal with linearly ordered base points is special *-simple.

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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: nlin