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Determining Integer-Valued Polynomials From Their Image

Vadim Ponomarenko — 2010

Actes des rencontres du CIRM

This note summarizes a presentation made at the Third International Meeting on Integer Valued Polynomials and Problems in Commutative Algebra. All the work behind it is joint with Scott T. Chapman, and will appear in []. Let Int ( ) represent the ring of polynomials with rational coefficients which are integer-valued at integers. We determine criteria for two such polynomials to have the same image set on .

Diversity in monoids

Jack ManeyVadim Ponomarenko — 2012

Czechoslovak Mathematical Journal

Let M be a (commutative cancellative) monoid. A nonunit element q M is called almost primary if for all a , b M , q a b implies that there exists k such that q a k or q b k . We introduce a new monoid invariant, diversity, which generalizes this almost primary property. This invariant is developed and contextualized with other monoid invariants. It naturally leads to two additional properties (homogeneity and strong homogeneity) that measure how far an almost primary element is from being primary. Finally, as an application...

Diversity in inside factorial monoids

Ulrich KrauseJack ManeyVadim Ponomarenko — 2012

Czechoslovak Mathematical Journal

In a recent paper (Diversity in Monoids, Czech. Math. J. 62 (2012), 795–809), the last two authors introduced and developed the monoid invariant “diversity” and related properties “homogeneity” and “strong homogeneity”. We investigate these properties within the context of inside factorial monoids, in which the diversity of an element counts the number of its different almost primary components. Inside factorial monoids are characterized via diversity and strong homogeneity. A new invariant complementary...

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