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Atomic density of arithmetical congruence monoids.
- Source :
-
Semigroup Forum . Apr2024, Vol. 108 Issue 2, p432-437. 6p. - Publication Year :
- 2024
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *MONOIDS
*DENSITY
*ARITHMETIC
*MULTIPLICATION
*ATOMS
*GEOMETRIC congruences
Subjects
Details
- Language :
- English
- ISSN :
- 00371912
- Volume :
- 108
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Semigroup Forum
- Publication Type :
- Academic Journal
- Accession number :
- 176995679
- Full Text :
- https://doi.org/10.1007/s00233-024-10426-w