Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: t-Reductions and t-integral closure of ideals   Let R be an integral domain and I a nonzero ideal of R. A sub-ideal J of I is
a t-reduction of I if (JI^{n})_{t}=(I^{n+1})_{t} for some positive integer n.
An element x in R is t-integral over I if there is an equation x^{n} +
a_{1}x^{n-1} +...+ a_{n-1}x + a_{n} = 0 with a_{i} in (I^{i})_{t} for I =
1,...,n. The set of all elements that are t-integral over I is called the
t-integral closure of I. This paper investigates the t-reductions and
t-integral closure of ideals. Our objective is to establish satisfactory
t-analogues of well-known results, in the literature, on the integral closure
of ideals and its correlation with reductions. Namely, Section 2 identifies
basic properties of t-reductions of ideals and features explicit examples
discriminating between the notions of reduction and t-reduction. Section 3
investigates the concept of t-integral closure of ideals, including its
correlation with t-reductions. Section 4 studies the persistence and
contraction of t-integral closure of ideals under ring homomorphisms. All along
the paper, the main results are illustrated with original examples.

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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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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: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph