NDLI: Diversity in monoids

Content Provider	Springer Nature Link
Author	Maney, Jack Pomarenko, Vadim
Copyright Year	2012
Abstract	Let M be a (commutative cancellative) monoid. A nonunit element q ∈ M is called almost primary if for all a, b ∈ M, q \| ab implies that there exists k ∈ ℕ 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 the authors consider factorizations into almost primary elements, which generalizes the established notion of factorization into primary elements.
Ending Page	809
Page Count	15
Starting Page	795
File Format	PDF
ISSN	00114642
e-ISSN	15729141
Journal	Czechoslovak Mathematical Journal
Issue Number	3
Volume Number	62
Language	English
Publisher	Springer-Verlag
Publisher Date	2012-10-18
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	diversity Ordinary Differential Equations Convex and Discrete Geometry Analysis Commutative semigroups Generalized primes and integers Mathematics Mathematical Modeling and Industrial Mathematics factorization monoid
Content Type	Text
Resource Type	Article
Subject	Mathematics

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Diversity in monoids