Non-commutative reduction rings.
Madlener, Klaus, Reinert, Birgit (1999)
Revista Colombiana de Matemáticas
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Displaying similar documents to “Integer-valued polynomials on algebras: a survey”
Non-commutative reduction rings.
Integral closures of ideals in the Rees ring
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The important ideas of reduction and integral closure of an ideal in a commutative Noetherian ring A (with identity) were introduced by Northcott and Rees [4]; a brief and direct approach to their theory is given in [6, (1.1)]. We begin by briefly summarizing some of the main aspects.
An example concerning the embedded primes associated with an ideal in the ring of polynomials.
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The purpose of my talk is to give an overview of some more or less recent developments on integer-valued polynomials and, doing so, to emphasize that integer-valued polynomials really occur in different areas: combinatorics, arithmetic, number theory, commutative and non-commutative algebra, topology, ultrametric analysis, and dynamics. I will show that several answers were given to open problems, and I will raise also some new questions.
Zero-divisors of content algebras
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In this article, we prove that in content extentions minimal primes extend to minimal primes and discuss zero-divisors of a content algebra over a ring who has Property (A) or whose set of zero-divisors is a finite union of prime ideals. We also examine the preservation of diameter of zero-divisor graph under content extensions.