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- Title
Atomic density of arithmetical congruence monoids.
- Authors
Olsson, Nils; O'Neill, Christopher; Rawling, Derek
- Abstract
Consider the set M a , b = { n ∈ Z ≥ 1 : n ≡ a mod b } ∪ { 1 } for a , b ∈ Z ≥ 1 . If a 2 ≡ a mod b , then M a , b is closed under multiplication and known as an arithmetic congruence monoid (ACM). A non-unit n ∈ M a , b is an atom if it cannot be expressed as a product of non-units, and the atomic density of M a , b is the limiting proportion of elements that are atoms. In this paper, we characterize the atomic density of M a , b in terms of a and b.
- Subjects
MONOIDS; DENSITY; ARITHMETIC; MULTIPLICATION; ATOMS; GEOMETRIC congruences
- Publication
Semigroup Forum, 2024, Vol 108, Issue 2, p432
- ISSN
0037-1912
- Publication type
Article
- DOI
10.1007/s00233-024-10426-w